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# Java 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.```

## 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.`

Output:

`Idempotent Matrix`

Time complexity: O(N3)

Auxiliary space: O(N2)

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