A sample matrix inversion in PHP using Gauss-Jordan elimination. This is implementation is meant for clarity, not for performance, memory usage, or numerical stability. You can optionally turn on the debug flag to output matrix state after every iteration. See https://en.wikipedia.org/wiki/Gauss-Jordan_elimination for more info. Enjoy!

test-matrix-invert.php

<?php

/**
 * Inverts a given matrix
 *
 * @param array $A matrix to invert
 * @param boolean $debug whether to print out debug info
 *
 * @return array inverted matrix
 */
function invert($A, $debug = FALSE)
{
	/// @todo check rows = columns

	$n = count($A);

	// get and append identity matrix
	$I = identity_matrix($n);
	for ($i = 0; $i < $n; ++ $i) {
		$A[$i] = array_merge($A[$i], $I[$i]);
	}

	if ($debug) {
		echo "\nStarting matrix: ";
		print_matrix($A);
	}

	// forward run
	for ($j = 0; $j < $n-1; ++ $j) {
		// for all remaining rows (diagonally)
		for ($i = $j+1; $i < $n; ++ $i) {
			// if the value is not already 0
			if ($A[$i][$j] !== 0) {
				// adjust scale to pivot row
				// subtract pivot row from current
				$scalar = $A[$j][$j] / $A[$i][$j];
				for ($jj = $j; $jj < $n*2; ++ $jj) {
					$A[$i][$jj] *= $scalar;
					$A[$i][$jj] -= $A[$j][$jj];
				}
			}
		}
		if ($debug) {
			echo "\nForward iteration $j: ";
			print_matrix($A);
		}
	}

	// reverse run
	for ($j = $n-1; $j > 0; -- $j) {
		for ($i = $j-1; $i >= 0; -- $i) {
			if ($A[$i][$j] !== 0) {
				$scalar = $A[$j][$j] / $A[$i][$j];
				for ($jj = $i; $jj < $n*2; ++ $jj) {
					$A[$i][$jj] *= $scalar;
					$A[$i][$jj] -= $A[$j][$jj];
				}
			}
		}
		if ($debug) {
			echo "\nReverse iteration $j: ";
			print_matrix($A);
		}
	}

	// last run to make all diagonal 1s
	/// @note this can be done in last iteration (i.e. reverse run) too!
	for ($j = 0; $j < $n; ++ $j) {
		if ($A[$j][$j] !== 1) {
			$scalar = 1 / $A[$j][$j];
			for ($jj = $j; $jj < $n*2; ++ $jj) {
				$A[$j][$jj] *= $scalar;
			}
		}
		if ($debug) {
			echo "\n1-out iteration $j: ";
			print_matrix($A);
		}
	}

	// take out the matrix inverse to return
	$Inv = array();
	for ($i = 0; $i < $n; ++ $i) {
		$Inv[$i] = array_slice($A[$i], $n);
	}

	return $Inv;
}

/**
 * Prints matrix
 *
 * @param array $A matrix
 * @param integer $decimals number of decimals
 */
function print_matrix($A, $decimals = 6)
{
	foreach ($A as $row) {
		echo "\n\t[";
		foreach ($row as $i) {
			echo "\t" . sprintf("%01.{$decimals}f", round($i, $decimals));
		}
		echo "\t]";
	}
}

/**
 * Produces an identity matrix of given size
 *
 * @param integer $n size of identity matrix
 *
 * @return array identity matrix
 */
function identity_matrix($n)
{
	$I = array();
	for ($i = 0; $i < $n; ++ $i) {
		for ($j = 0; $j < $n; ++ $j) {
			$I[$i][$j] = ($i == $j) ? 1 : 0;
		}
	}
	return $I;
}

$A = array(
	array( 10, -15,  30,   6, -8 ),
	array(  0,  -4,  60,  11, -5 ),
	array(  8,   9,   2,   3,  7 ),
	array( 25,  10,  -9,   9,  0 ),
	array( 13,   3, -12,   5,  2 ),
);

echo "\nMatrix:";
print_matrix($A);
echo "\n";

$B = invert($A);

echo "\nInversion result:";
print_matrix($B);
echo "\n\n";

?>

If the matrix has a zero in it, this doesn't work. For instance try do the inverse of a 3x3 identity matrix. It should return the 3x3 identity matrix but it fails...

@pauloz1890 thanks for pointing that out! I fixed it to work with 0 values too in 2nd revision.

Good morning, I have a problem . I would like to inform as parameter a matrix that way , but I can not .
for ($i=0; $i <5 ; $i++) {
for ($j=0; $j< 5 ; $j++) {
$Matrix[$i][$j] = 4;}
}

$invM = invert($Matrix); <- Don't work.

Because I can only pass a parameter that way?

$Matrix = [[4,4,4,4],[4,4,4,4],[4,4,4,4],[4,4,4,4]];
$invM = invert($Matrix); <- work

Can you help me ?

Hi @rigelcastro - the matrix you specified does not have an inverse. Here's the output from octave:

octave:1> inv([4,4,4,4; 4,4,4,4; 4,4,4,4; 4,4,4,4])
warning: inverse: matrix singular to machine precision, rcond = 0
ans =

   Inf   Inf   Inf   Inf
   Inf   Inf   Inf   Inf
   Inf   Inf   Inf   Inf
   Inf   Inf   Inf   Inf

In my implementation we don't get such nice output, but instead we get a division by 0 warning from PHP. This can be made better.

Crashes on division by zero for:
$A = [
[1, 0, 7],
[0, 2, 0],
[0, 0, 3],
];