MathPHP\LinearAlgebra\Matrix::inverse PHP Method

    public function inverse() : Matrix
    {
        if (isset($this->A⁻¹)) {
            return $this->A⁻¹;
        }
        if (!$this->isSquare()) {
            throw new Exception\MatrixException('Not a sqaure matrix (required for determinant)');
        }
        $│A│ = $this->det ?? $this->det();
        if ($│A│ == 0) {
            throw new Exception\MatrixException('Singular matrix (determinant = 0); not invertible');
        }
        $m = $this->m;
        $n = $this->n;
        $A = $this->A;
        /*
         * 2x2 matrix:
         *      [a b]
         *  A = [c d]
         *
         *        1
         * A⁻¹ = --- [d -b]
         *       │A│ [-c a]
         */
        if ($m === 2) {
            $a = $A[0][0];
            $b = $A[0][1];
            $c = $A[1][0];
            $d = $A[1][1];
            $R = MatrixFactory::create([[$d, -$b], [-$c, $a]]);
            $A⁻¹ = $R->scalarMultiply(1 / $│A│);
            $this->A⁻¹ = $A⁻¹;
            return $A⁻¹;
        }
        /*
         * nxn matrix 3x3 or larger
         */
        $R = $this->augmentIdentity()->rref();
        $A⁻¹ = [];
        for ($i = 0; $i < $n; $i++) {
            $A⁻¹[$i] = array_slice($R[$i], $n);
        }
        $A⁻¹ = MatrixFactory::create($A⁻¹);
        $this->A⁻¹ = $A⁻¹;
        return $A⁻¹;
    }