# Matrix Multiplication | Recursive

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
```

## Recommended: Please try your approach on {IDE} first, before moving on to the solution.

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.

## C/C++

```// Recursive code for Matrix Multiplication
#include <stdio.h>

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;
}
```

## 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
```

Output:

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

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