Javascript Program to check Involutory Matrix

Given a matrix and the task is to check matrix is involutory matrix or not. 
Involutory Matrix: A matrix is said to be involutory matrix if matrix multiply by itself return the identity matrix. Involutory matrix is the matrix that is its own inverse. The matrix A is said to be involutory matrix if A * A = I. Where I is the identity matrix. 

Examples:

Input : mat[N][N] = {{1, 0, 0},
                     {0, -1, 0},
                     {0, 0, -1}}
Output : Involutory Matrix

Input : mat[N][N] = {{1, 0, 0},
                     {0, 1, 0},
                     {0, 0, 1}} 
Output : Involutory Matrix

Javascript

<script>

// Javascript to implement involutory matrix.
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];
        }
    }
}

// Function to check involutory matrix.
function InvolutoryMatrix(mat)
{
    var res = Array(N).fill(0).map(
        x => Array(N).fill(0));

    // Multiply function call.
    multiply(mat, res);

    for(var i = 0; i < N; i++)
    {
        for(var j = 0; j < N; j++)
        {
            if (i == j && res[i][j] != 1)
                return false;
            if (i != j && res[i][j] != 0)
                return false;
        }
    }
    return true;
}

// Driver code
var mat = [ [ 1, 0, 0 ],
            [ 0, -1, 0 ],
            [ 0, 0, -1 ] ];

// Function call. If function return
// true then if part will execute
// otherwise else part will execute.
if (InvolutoryMatrix(mat))
    document.write("Involutory Matrix");
else
    document.write("Not Involutory Matrix");

// This code is contributed by 29AjayKumar

</script>

Output :

Involutory Matrix

Time complexity: O(N³) as three nested loops are executing. Here N is size of rows and columns.
Auxiliary space: O(N²) as res 2d matrix has been created.

Please refer complete article on Program to check Involutory Matrix for more details!