# Program to check idempotent matrix

Given a N * N matrix and the task is to check matrix is idempotent matrix or not.

Idempotent matrix: A matrix is said to be idempotent matrix if matrix multiplied by itself return the same matrix. The matrix M is said to be idempotent matrix if and only if M * M = M. In idempotent matrix M is a square matrix.

Examples:

```Input : mat[][] = {{3, -6},
{1, -2}};
Output : Idempotent Matrix

Input : mat[N][N] = {{2, -2, -4},
{-1, 3, 4},
{1, -2, -3}}
Output : Idempotent Matrix.
```

## C++

 `// Program to check given matrix  ` `// is idempotent matrix or not. ` `#include ` `#define N 3 ` `using` `namespace` `std; ` ` `  `// Function for matrix multiplication. ` `void` `multiply(``int` `mat[][N], ``int` `res[][N]) ` `{ ` `    ``for` `(``int` `i = 0; i < N; i++) ` `    ``{ ` `        ``for` `(``int` `j = 0; j < N; j++) ` `        ``{ ` `            ``res[i][j] = 0; ` `            ``for` `(``int` `k = 0; k < N; k++) ` `                ``res[i][j] += mat[i][k] * mat[k][j]; ` `        ``} ` `    ``} ` `} ` ` `  `// Function to check idempotent ` `// property of matrix. ` `bool` `checkIdempotent(``int` `mat[][N]) ` `{    ` `    ``// Calculate multiplication of matrix ` `    ``// with itself and store it into res. ` `    ``int` `res[N][N]; ` `    ``multiply(mat, res); ` ` `  `    ``for` `(``int` `i = 0; i < N; i++)     ` `        ``for` `(``int` `j = 0; j < N; j++)         ` `            ``if` `(mat[i][j] != res[i][j]) ` `                ``return` `false``; ` `    ``return` `true``; ` `} ` ` `  `// Driver function. ` `int` `main() ` `{ ` `    ``int` `mat[N][N] = {{2, -2, -4}, ` `                    ``{-1, 3, 4}, ` `                    ``{1, -2, -3}}; ` `     `  `    ``// checkIdempotent function call. ` `    ``if` `(checkIdempotent(mat)) ` `        ``cout << ``"Idempotent Matrix"``; ` `    ``else` `        ``cout << ``"Not Idempotent Matrix."``; ` `    ``return` `0; ` `} `

## Java

 `// Java program to check given matrix  ` `// is idempotent matrix or not. ` `import` `java.io.*; ` ` `  `class` `GFG  ` `{ ` `    ``static` `int` `N = ``3``; ` `     `  `    ``// Function for matrix multiplication. ` `    ``static` `void` `multiply(``int` `mat[][], ``int` `res[][]) ` `    ``{ ` `        ``for` `(``int` `i = ``0``; i < N; i++) ` `        ``{ ` `            ``for` `(``int` `j = ``0``; j < N; j++) ` `            ``{ ` `                ``res[i][j] = ``0``; ` `                ``for` `(``int` `k = ``0``; k < N; k++) ` `                    ``res[i][j] += mat[i][k] * mat[k][j]; ` `            ``} ` `        ``} ` `    ``} ` `     `  `    ``// Function to check idempotent ` `    ``// property of matrix. ` `    ``static` `boolean` `checkIdempotent(``int` `mat[][]) ` `    ``{  ` `        ``// Calculate multiplication of matrix ` `        ``// with itself and store it into res. ` `        ``int` `res[][] = ``new` `int``[N][N]; ` `        ``multiply(mat, res); ` `     `  `        ``for` `(``int` `i = ``0``; i < N; i++) ` `        ``{  ` `            ``for` `(``int` `j = ``0``; j < N; j++) ` `            ``{ ` `                ``if` `(mat[i][j] != res[i][j]) ` `                    ``return` `false``; ` `            ``} ` `        ``} ` `        ``return` `true``; ` `    ``} ` ` `  `    ``// Driver code. ` `    ``public` `static` `void` `main (String[] args)  ` `    ``{ ` `        ``int` `mat[][] = {{``2``, -``2``, -``4``}, ` `                       ``{-``1``, ``3``, ``4``}, ` `                       ``{``1``, -``2``, -``3``}}; ` `     `  `        ``// checkIdempotent function call. ` `        ``if` `(checkIdempotent(mat)) ` `            ``System.out.println( ``"Idempotent Matrix"``); ` `        ``else` `            ``System.out.println(``"Not Idempotent Matrix."``); ` `         `  `    ``} ` `} ` ` `  `// This code is contributed by vt_m. `

## Python 3

 `# Python Program to check given matrix  ` `# is idempotent matrix or not. ` `import` `math ` ` `  `# Function for matrix multiplication. ` `def` `multiply(mat, res): ` ` `  `    ``N``=` `len``(mat) ` `    ``for` `i ``in` `range``(``0``,N): ` `     `  `        ``for` `j ``in` `range``(``0``,N): ` `         `  `            ``res[i][j] ``=` `0` `            ``for` `k ``in` `range``(``0``,N): ` `                ``res[i][j] ``+``=` `mat[i][k] ``*` `mat[k][j] ` ` `  `# Function to check idempotent ` `# property of matrix. ` `def` `checkIdempotent(mat): ` ` `  `    ``N``=` `len``(mat) ` `    ``# Calculate multiplication of matrix ` `    ``# with itself and store it into res. ` `    ``res ``=``[[``0``]``*``N ``for` `i ``in` `range``(``0``,N)] ` `    ``multiply(mat, res) ` ` `  `    ``for` `i ``in` `range``(``0``,N): ` `        ``for` `j ``in` `range``(``0``,N):      ` `            ``if` `(mat[i][j] !``=` `res[i][j]): ` `                ``return` `False` `    ``return` `True` ` `  `# driver Function ` `mat ``=` `[ [``2``, ``-``2``, ``-``4``], ` `        ``[``-``1``, ``3``, ``4``], ` `        ``[``1``, ``-``2``, ``-``3``] ] ` `     `  `# checkIdempotent function call. ` `if` `(checkIdempotent(mat)): ` `    ``print``(``"Idempotent Matrix"``) ` `else``: ` `    ``print``(``"Not Idempotent Matrix."``) ` ` `  `# This code is contributed by Gitanjali. `

## C#

 `// C# program to check given matrix  ` `// is idempotent matrix or not. ` `using` `System; ` ` `  `class` `GFG  ` `{ ` `    ``static` `int` `N = 3; ` `     `  `    ``// Function for matrix multiplication. ` `    ``static` `void` `multiply(``int` `[,]mat, ``int` `[,]res) ` `    ``{ ` `        ``for` `(``int` `i = 0; i < N; i++) ` `        ``{ ` `            ``for` `(``int` `j = 0; j < N; j++) ` `            ``{ ` `                ``res[i,j] = 0; ` `                ``for` `(``int` `k = 0; k < N; k++) ` `                    ``res[i,j] += mat[i,k] * mat[k,j]; ` `            ``} ` `        ``} ` `    ``} ` `     `  `    ``// Function to check idempotent ` `    ``// property of matrix. ` `    ``static` `bool` `checkIdempotent(``int` `[,]mat) ` `    ``{  ` `        ``// Calculate multiplication of matrix ` `        ``// with itself and store it into res. ` `        ``int` `[,]res = ``new` `int``[N,N]; ` `        ``multiply(mat, res); ` `     `  `        ``for` `(``int` `i = 0; i < N; i++) ` `        ``{  ` `            ``for` `(``int` `j = 0; j < N; j++) ` `            ``{ ` `                ``if` `(mat[i,j] != res[i,j]) ` `                    ``return` `false``; ` `            ``} ` `        ``} ` `        ``return` `true``; ` `    ``} ` ` `  `    ``// Driver code ` `    ``public` `static` `void` `Main ()  ` `    ``{ ` `        ``int` `[,]mat = {{2, -2, 4}, ` `                    ``{-1, 3, 4}, ` `                    ``{1, -2, -3}}; ` `     `  `        ``// checkIdempotent function call. ` `        ``if` `(checkIdempotent(mat)) ` `            ``Console.WriteLine( ``"Idempotent Matrix"``); ` `        ``else` `            ``Console.WriteLine(``"Not Idempotent Matrix."``); ` `         `  `    ``} ` `} ` ` `  `// This code is contributed by vt_m. `

Output

`Idempotent Matrix`

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