MathPHP\LinearAlgebra\Matrix::det PHP Method

    public function det()
    {
        if (isset($this->det)) {
            return $this->det;
        }
        if (!$this->isSquare()) {
            throw new Exception\MatrixException('Not a sqaure matrix (required for determinant)');
        }
        $m = $this->m;
        $n = $this->n;
        $R = MatrixFactory::create($this->A);
        /*
         * 1x1 matrix
         *  A = [a]
         *
         * |A| = a
         */
        if ($m === 1) {
            $this->det = $R[0][0];
            return $this->det;
        }
        /*
         * 2x2 matrix
         *      [a b]
         *  A = [c d]
         *
         * |A| = ad - bc
         */
        if ($m === 2) {
            $a = $R[0][0];
            $b = $R[0][1];
            $c = $R[1][0];
            $d = $R[1][1];
            $ad = $a * $d;
            $bc = $b * $c;
            $this->det = $ad - $bc;
            return $this->det;
        }
        /*
         * 3x3 matrix
         *      [a b c]
         *  A = [d e f]
         *      [g h i]
         *
         * |A| = a(ei - fh) - b(di - fg) + c(dh - eg)
         */
        if ($m === 3) {
            $a = $R[0][0];
            $b = $R[0][1];
            $c = $R[0][2];
            $d = $R[1][0];
            $e = $R[1][1];
            $f = $R[1][2];
            $g = $R[2][0];
            $h = $R[2][1];
            $i = $R[2][2];
            $ei = $e * $i;
            $fh = $f * $h;
            $di = $d * $i;
            $fg = $f * $g;
            $dh = $d * $h;
            $eg = $e * $g;
            $this->det = $a * ($ei - $fh) - $b * ($di - $fg) + $c * ($dh - $eg);
            return $this->det;
        }
        /*
         * nxn matrix 4x4 or larger
         * Get row reduced echelon form, then compute determinant of rref.
         * Then plug into formula with swaps and product of scaling factor.
         * │A│ = (-1)ⁿ │rref(A)│ ∏1/k
         */
        $rref⟮A⟯ = $this->rref ?? $this->rref();
        $ⁿ = $this->rref_swaps;
        $∏1／k = $this->rref_∏scaling_factor;
        // Det(rref(A))
        $│rref⟮A⟯│ = 1;
        for ($i = 0; $i < $m; $i++) {
            $│rref⟮A⟯│ *= $rref⟮A⟯[$i][$i];
        }
        // │A│ = (-1)ⁿ │rref(A)│ ∏1/k
        $this->det = (-1) ** $ⁿ * ($│rref⟮A⟯│ / $∏1／k);
        return $this->det;
    }