JavaScript Program to Find the Determinant of a Matrix

// N is the Order of the matrix
let N = 3;

// Recursive function to find determinant
function determinantOfMatrixRecursive(mat, n) {
    if (n === 1) {
        return mat[0][0];
    }
    let det = 0;
    let sign = 1;
    for (let i = 0; i < n; i++) {
        let submatrix = 
            createSubmatrix(mat, i, n);
        det += sign * mat[0][i] * 
            determinantOfMatrixRecursive(submatrix, n - 1);
        sign = -sign;
    }
    return det;
}

// Function to find sub-matrices of different orders
function createSubmatrix(mat, colToRemove, n) {
    let submatrix = [];
    for (let i = 1; i < n; i++) {
        let newRow = [];
        for (let j = 0; j < n; j++) {
            if (j !== colToRemove) {
                newRow.push(mat[i][j]);
            }
        }
        submatrix.push(newRow);
    }
    return submatrix;
}

let mat = [
    [0, 4, -1],
    [0, 0, -2],
    [1, 2, -1]
];
console.log(
    "Determinant of the matrix is : ",
    determinantOfMatrixRecursive(mat, N)
);

// N is the order of the matrix
const N = 3;

function determinantOfMatrixIterative(mat, n) {
    let det = 1;
    let total = 1;
    const temp = Array(n).fill(0);
    for (let i = 0; i < n; i++) {
        let index = i;
        while (index < n && mat[index][i] === 0) {
            index++;
        }
        if (index === n) {
            continue;
        }
        if (index !== i) {
            for (let j = 0; j < n; j++) {
                [mat[i][j], mat[index][j]] = 
                [mat[index][j], mat[i][j]];
            }
            det *= Math.pow(-1, index - i);
        }
        for (let j = 0; j < n; j++) {
            temp[j] = mat[i][j];
        }
        for (let j = i + 1; j < n; j++) {
            const num1 = temp[i];
            const num2 = mat[j][i];
            for (let k = 0; k < n; k++) {
                mat[j][k] = 
                    num1 * mat[j][k] - 
                    num2 * temp[k];
            }
            total *= num1;
        }
    }
    for (let i = 0; i < n; i++) {
        det *= mat[i][i];
    }
    return det / total;
}

const mat = [
    [8, 1, 2],
    [2, 1, 4],
    [1, 0, 5]
];
console.log(
    "Determinant of the matrix is:", 
    determinantOfMatrixIterative(mat, N));