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 codevar 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!
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