# Matrix Multiplication | Recursive

• Difficulty Level : Medium
• Last Updated : 14 Jun, 2022

Given two matrices A and B. The task is to multiply matrix A and matrix B recursively. If matrix A and matrix B are not multiplicative compatible, then generate output “Not Possible”.
Examples :

```Input: A = 12 56
45 78
B = 2 6
5 8
Output: 304 520
480 894

Input: A = 1 2 3
4 5 6
7 8 9
B = 1 2 3
4 5 6
7 8 9

Output: 30  36  42
66  81  96
102 126 150  ```

It is recommended to first refer Iterative Matrix Multiplication.
First check if multiplication between matrices is possible or not. For this, check if number of columns of first matrix is equal to number of rows of second matrix or not. If both are equal than proceed further otherwise generate output “Not Possible”.
In Recursive Matrix Multiplication, we implement three loops of Iteration through recursive calls. The inner most Recursive call of multiplyMatrix() is to iterate k (col1 or row2). The second recursive call of multiplyMatrix() is to change the columns and the outermost recursive call is to change rows.
Below is Recursive Matrix Multiplication code.

## Java

 `// Java recursive code for Matrix Multiplication` `class` `GFG``{``    ``public` `static` `int` `MAX = ``100``;``    ` `    ``// Note that below variables are static``    ``// i and j are used to know current cell of``    ``// result matrix C[][]. k is used to know``    ``// current column number of A[][] and row``    ``// number of B[][] to be multiplied``    ``public` `static` `int` `i = ``0``, j = ``0``, k = ``0``;``    ` `    ``static` `void` `multiplyMatrixRec(``int` `row1, ``int` `col1, ``int` `A[][],``                       ``int` `row2, ``int` `col2, ``int` `B[][],``                       ``int` `C[][])``    ``{``        ``// If all rows traversed``        ``if` `(i >= row1)``            ``return``;`` ` `        ``// If i < row1``        ``if` `(j < col2)``        ``{``            ``if` `(k < col1)``            ``{``                ``C[i][j] += A[i][k] * B[k][j];``                ``k++;`` ` `                ``multiplyMatrixRec(row1, col1, A, row2, col2, B, C);``            ``}`` ` `            ``k = ``0``;``            ``j++;``            ``multiplyMatrixRec(row1, col1, A, row2, col2, B, C);``        ``}`` ` `        ``j = ``0``;``        ``i++;``        ``multiplyMatrixRec(row1, col1, A, row2, col2, B, C);``    ``}`` ` `    ``// Function to multiply two matrices A[][] and B[][]``    ``static` `void` `multiplyMatrix(``int` `row1, ``int` `col1, ``int` `A[][],``                    ``int` `row2, ``int` `col2, ``int` `B[][])``    ``{``        ``if` `(row2 != col1)``        ``{``            ``System.out.println(``"Not Possible\n"``);``            ``return``;``        ``}`` ` `        ``int``[][] C = ``new` `int``[MAX][MAX];`` ` `        ``multiplyMatrixRec(row1, col1, A, row2, col2, B, C);`` ` `        ``// Print the result``        ``for` `(``int` `i = ``0``; i < row1; i++)``        ``{``            ``for` `(``int` `j = ``0``; j < col2; j++)``                ``System.out.print(C[i][j]+``" "``);`` ` `            ``System.out.println();``        ``}``    ``}``    ` `    ``// driver program``    ``public` `static` `void` `main (String[] args)``    ``{``        ``int` `row1 = ``3``, col1 = ``3``, row2 = ``3``, col2 = ``3``;``        ``int` `A[][] = { {``1``, ``2``, ``3``},``                      ``{``4``, ``5``, ``6``},``                      ``{``7``, ``8``, ``9``}};`` ` `        ``int` `B[][] = { {``1``, ``2``, ``3``},``                      ``{``4``, ``5``, ``6``},``                      ``{``7``, ``8``, ``9``} };`` ` `        ``multiplyMatrix(row1, col1, A, row2, col2, B);``    ``}``}` `// Contributed by Pramod Kumar`

## Python3

 `# Recursive code for Matrix Multiplication``MAX` `=` `100``i ``=` `0``j ``=` `0``k ``=` `0` `def` `multiplyMatrixRec(row1, col1, A,``                      ``row2, col2, B, C):``                          ` `    ``# Note that below variables are static``    ``# i and j are used to know current cell of``    ``# result matrix C[][]. k is used to know``    ``# current column number of A[][] and row``    ``# number of B[][] to be multiplied``    ``global` `i``    ``global` `j``    ``global` `k``    ` `    ``# If all rows traversed.``    ``if` `(i >``=` `row1):``        ``return``        ` `    ``# If i < row1``    ``if` `(j < col2):``        ``if` `(k < col1):``            ``C[i][j] ``+``=` `A[i][k] ``*` `B[k][j]``            ``k ``+``=` `1``            ``multiplyMatrixRec(row1, col1, A,``                              ``row2, col2,B, C)` `        ``k ``=` `0``        ``j ``+``=` `1``        ``multiplyMatrixRec(row1, col1, A,``                          ``row2, col2, B, C)` `    ``j ``=` `0``    ``i ``+``=` `1``    ``multiplyMatrixRec(row1, col1, A,``                      ``row2, col2, B, C)` `# Function to multiply two matrices``# A[][] and B[][]``def` `multiplyMatrix(row1, col1, A, row2, col2, B):``    ``if` `(row2 !``=` `col1):``        ``print``(``"Not Possible"``)``        ``return` `    ``C ``=` `[[``0` `for` `i ``in` `range``(``MAX``)]``            ``for` `i ``in` `range``(``MAX``)]``    ``multiplyMatrixRec(row1, col1, A,``                      ``row2, col2, B, C)``    ` `    ``# Print the result``    ``for` `i ``in` `range``(row1):``        ``for` `j ``in` `range``(col2):``            ``print``( C[i][j], end ``=` `" "``)``        ``print``()` `# Driver Code``A ``=` `[[``1``, ``2``, ``3``],``     ``[``4``, ``5``, ``6``],``     ``[``7``, ``8``, ``9``]]``B ``=` `[[``1``, ``2``, ``3``],``     ``[``4``, ``5``, ``6``],``     ``[``7``, ``8``, ``9``]]` `row1 ``=` `3``col1 ``=` `3``row2 ``=` `3``col2 ``=` `3``multiplyMatrix(row1, col1, A, row2, col2, B)` `# This code is contributed by sahilshelangia`

## C#

 `// C# recursive code for``// Matrix Multiplication``using` `System;` `class` `GFG``{``    ``public` `static` `int` `MAX = 100;``    ` `    ``// Note that below variables``    ``// are static i and j are used``    ``// to know current cell of result``    ``// matrix C[][]. k is used to``    ``// know current column number of``    ``// A[][] and row number of B[][]``    ``// to be multiplied``    ``public` `static` `int` `i = 0, j = 0, k = 0;``    ` `    ``static` `void` `multiplyMatrixRec(``int` `row1, ``int` `col1,``                                  ``int` `[,]A, ``int` `row2,``                                  ``int` `col2, ``int` `[,]B,``                                  ``int` `[,]C)``    ``{``        ``// If all rows traversed``        ``if` `(i >= row1)``            ``return``;` `        ``// If i < row1``        ``if` `(j < col2)``        ``{``            ``if` `(k < col1)``            ``{``                ``C[i, j] += A[i, k] * B[k, j];``                ``k++;` `                ``multiplyMatrixRec(row1, col1, A,``                                  ``row2, col2, B, C);``            ``}` `            ``k = 0;``            ``j++;``            ``multiplyMatrixRec(row1, col1, A,``                              ``row2, col2, B, C);``        ``}` `        ``j = 0;``        ``i++;``        ``multiplyMatrixRec(row1, col1, A,``                          ``row2, col2, B, C);``    ``}` `    ``// Function to multiply two``    ``// matrices A[][] and B[][]``    ``static` `void` `multiplyMatrix(``int` `row1, ``int` `col1,``                               ``int` `[,]A, ``int` `row2,``                               ``int` `col2, ``int` `[,]B)``    ``{``        ``if` `(row2 != col1)``        ``{``            ``Console.WriteLine(``"Not Possible\n"``);``            ``return``;``        ``}` `        ``int``[,]C = ``new` `int``[MAX, MAX];` `        ``multiplyMatrixRec(row1, col1, A,``                          ``row2, col2, B, C);` `        ``// Print the result``        ``for` `(``int` `i = 0; i < row1; i++)``        ``{``            ``for` `(``int` `j = 0; j < col2; j++)``                ``Console.Write(C[i, j] + ``" "``);` `            ``Console.WriteLine();``        ``}``    ``}``    ` `    ``// Driver Code``    ``static` `public` `void` `Main ()``    ``{``        ``int` `row1 = 3, col1 = 3,``            ``row2 = 3, col2 = 3;``        ``int` `[,]A = {{1, 2, 3},``                    ``{4, 5, 6},``                    ``{7, 8, 9}};` `        ``int` `[,]B = {{1, 2, 3},``                    ``{4, 5, 6},``                    ``{7, 8, 9}};` `        ``multiplyMatrix(row1, col1, A,``                       ``row2, col2, B);``    ``}``}` `// This code is contributed by m_kit`

## Javascript

 ``

## C++

 `// Recursive code for Matrix Multiplication``#include ` `const` `int` `MAX = 100;` `void` `multiplyMatrixRec(``int` `row1, ``int` `col1, ``int` `A[][MAX],``                       ``int` `row2, ``int` `col2, ``int` `B[][MAX],``                       ``int` `C[][MAX])``{``    ``// Note that below variables are static``    ``// i and j are used to know current cell of``    ``// result matrix C[][]. k is used to know``    ``// current column number of A[][] and row``    ``// number of B[][] to be multiplied``    ``static` `int` `i = 0, j = 0, k = 0;` `    ``// If all rows traversed.``    ``if` `(i >= row1)``        ``return``;` `    ``// If i < row1``    ``if` `(j < col2) {``        ``if` `(k < col1) {``            ``C[i][j] += A[i][k] * B[k][j];``            ``k++;` `            ``multiplyMatrixRec(row1, col1, A, row2, col2, B,``                              ``C);``        ``}` `        ``k = 0;``        ``j++;``        ``multiplyMatrixRec(row1, col1, A, row2, col2, B, C);``    ``}` `    ``j = 0;``    ``i++;``    ``multiplyMatrixRec(row1, col1, A, row2, col2, B, C);``}` `// Function to multiply two matrices A[][] and B[][]``void` `multiplyMatrix(``int` `row1, ``int` `col1, ``int` `A[][MAX],``                    ``int` `row2, ``int` `col2, ``int` `B[][MAX])``{``    ``if` `(row2 != col1) {``        ``printf``(``"Not Possible\n"``);``        ``return``;``    ``}` `    ``int` `C[MAX][MAX] = { 0 };` `    ``multiplyMatrixRec(row1, col1, A, row2, col2, B, C);` `    ``// Print the result``    ``for` `(``int` `i = 0; i < row1; i++) {``        ``for` `(``int` `j = 0; j < col2; j++)``            ``printf``(``"%d  "``, C[i][j]);` `        ``printf``(``"\n"``);``    ``}``}` `// Driven Program``int` `main()``{``    ``int` `A[][MAX]``        ``= { { 1, 2, 3 }, { 4, 5, 6 }, { 7, 8, 9 } };` `    ``int` `B[][MAX]``        ``= { { 1, 2, 3 }, { 4, 5, 6 }, { 7, 8, 9 } };` `    ``int` `row1 = 3, col1 = 3, row2 = 3, col2 = 3;``    ``multiplyMatrix(row1, col1, A, row2, col2, B);` `    ``return` `0;``}` `// This code is contributed by Aarti_Rathi`

Output :

```30  36  42
66  81  96
102  126  150  ```

Time Complexity: O(row1 * col2)
Auxiliary Space: O(log (max(row1,col2)), As implicit stack is used due to recursion

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