Javascript Program to check idempotent matrix

Given an N * N matrix and the task is to check matrix is an idempotent matrix or not.
Idempotent matrix: A matrix is said to be an idempotent matrix if the matrix multiplied by itself returns the same matrix. The matrix M is said to be an idempotent matrix if and only if M * M = M. In an 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.

Javascript

<script>

// Javascript program to check given matrix
// is idempotent matrix or not.
var N = 3;

// Function for matrix multiplication.
function multiply(mat, res)
{
    for (var i = 0; i < N; i++)
    {
        for (var j = 0; j < N; j++)
        {
            res[i][j] = 0;
            for (var k = 0; k < N; k++)
                res[i][j] += mat[i][k] * mat[k][j];
        }
    }
    return res;
}

// Function to check idempotent
// property of matrix.
function checkIdempotent(mat)
{

    // Calculate multiplication of matrix
    // with itself and store it into res.
    var res = Array.from(Array(N), ()=>Array(N).fill(0));
    res = multiply(mat, res);

    for (var i = 0; i < N; i++)
    {
        for (var j = 0; j < N; j++)
        {
            if (mat[i][j] != res[i][j])
                return false;
        }
    }
    return true;
}

// Driver code
var mat = [[2, -2, -4],
            [-1, 3, 4],
            [1, -2, -3]];

// checkIdempotent function call.
if (checkIdempotent(mat))
    document.write( "Idempotent Matrix");
else
    document.write("Not Idempotent Matrix.");

// This code is contributed by noob2000.
</script>

Output:

Idempotent Matrix

Time Complexity: O(N³)
Auxiliary Space: O(N²)

Please refer complete article on Program to check idempotent matrix for more details!