MEL and Python procedure to invert a 4x4 matrix in Maya

Some may ask: "But, why??". To that, I would answer: "Why not?" 💩

proc float[] invertRowMajor(float $m[])
{
    float $invOut[17];
    // Extra element to indicate if the inversion failed or not:
    $invOut[16] = 1;
    
    float $inv[16];    
  
    $inv[ 0] =  $m[5] * $m[10] * $m[15] - $m[5] * $m[14] * $m[11] - $m[6] * $m[9] * $m[15] + $m[6] * $m[13] * $m[11] + $m[7] * $m[9] * $m[14] - $m[7] * $m[13] * $m[10];
    $inv[ 1] = -$m[1] * $m[10] * $m[15] + $m[1] * $m[14] * $m[11] + $m[2] * $m[9] * $m[15] - $m[2] * $m[13] * $m[11] - $m[3] * $m[9] * $m[14] + $m[3] * $m[13] * $m[10];
    $inv[ 2] =  $m[1] * $m[ 6] * $m[15] - $m[1] * $m[14] * $m[ 7] - $m[2] * $m[5] * $m[15] + $m[2] * $m[13] * $m[ 7] + $m[3] * $m[5] * $m[14] - $m[3] * $m[13] * $m[ 6];
    $inv[ 3] = -$m[1] * $m[ 6] * $m[11] + $m[1] * $m[10] * $m[ 7] + $m[2] * $m[5] * $m[11] - $m[2] * $m[ 9] * $m[ 7] - $m[3] * $m[5] * $m[10] + $m[3] * $m[ 9] * $m[ 6];
    $inv[ 4] = -$m[4] * $m[10] * $m[15] + $m[4] * $m[14] * $m[11] + $m[6] * $m[8] * $m[15] - $m[6] * $m[12] * $m[11] - $m[7] * $m[8] * $m[14] + $m[7] * $m[12] * $m[10];
    $inv[ 5] =  $m[0] * $m[10] * $m[15] - $m[0] * $m[14] * $m[11] - $m[2] * $m[8] * $m[15] + $m[2] * $m[12] * $m[11] + $m[3] * $m[8] * $m[14] - $m[3] * $m[12] * $m[10];
    $inv[ 6] = -$m[0] * $m[ 6] * $m[15] + $m[0] * $m[14] * $m[ 7] + $m[2] * $m[4] * $m[15] - $m[2] * $m[12] * $m[ 7] - $m[3] * $m[4] * $m[14] + $m[3] * $m[12] * $m[ 6];
    $inv[ 7] =  $m[0] * $m[ 6] * $m[11] - $m[0] * $m[10] * $m[ 7] - $m[2] * $m[4] * $m[11] + $m[2] * $m[ 8] * $m[ 7] + $m[3] * $m[4] * $m[10] - $m[3] * $m[ 8] * $m[ 6];
    $inv[ 8] =  $m[4] * $m[ 9] * $m[15] - $m[4] * $m[13] * $m[11] - $m[5] * $m[8] * $m[15] + $m[5] * $m[12] * $m[11] + $m[7] * $m[8] * $m[13] - $m[7] * $m[12] * $m[ 9];
    $inv[ 9] = -$m[0] * $m[ 9] * $m[15] + $m[0] * $m[13] * $m[11] + $m[1] * $m[8] * $m[15] - $m[1] * $m[12] * $m[11] - $m[3] * $m[8] * $m[13] + $m[3] * $m[12] * $m[ 9];
    $inv[10] =  $m[0] * $m[ 5] * $m[15] - $m[0] * $m[13] * $m[ 7] - $m[1] * $m[4] * $m[15] + $m[1] * $m[12] * $m[ 7] + $m[3] * $m[4] * $m[13] - $m[3] * $m[12] * $m[ 5];
    $inv[11] = -$m[0] * $m[ 5] * $m[11] + $m[0] * $m[ 9] * $m[ 7] + $m[1] * $m[4] * $m[11] - $m[1] * $m[ 8] * $m[ 7] - $m[3] * $m[4] * $m[ 9] + $m[3] * $m[ 8] * $m[ 5];
    $inv[12] = -$m[4] * $m[ 9] * $m[14] + $m[4] * $m[13] * $m[10] + $m[5] * $m[8] * $m[14] - $m[5] * $m[12] * $m[10] - $m[6] * $m[8] * $m[13] + $m[6] * $m[12] * $m[ 9];
    $inv[13] =  $m[0] * $m[ 9] * $m[14] - $m[0] * $m[13] * $m[10] - $m[1] * $m[8] * $m[14] + $m[1] * $m[12] * $m[10] + $m[2] * $m[8] * $m[13] - $m[2] * $m[12] * $m[ 9];
    $inv[14] = -$m[0] * $m[ 5] * $m[14] + $m[0] * $m[13] * $m[ 6] + $m[1] * $m[4] * $m[14] - $m[1] * $m[12] * $m[ 6] - $m[2] * $m[4] * $m[13] + $m[2] * $m[12] * $m[ 5];
    $inv[15] =  $m[0] * $m[ 5] * $m[10] - $m[0] * $m[ 9] * $m[ 6] - $m[1] * $m[4] * $m[10] + $m[1] * $m[ 8] * $m[ 6] + $m[2] * $m[4] * $m[ 9] - $m[2] * $m[ 8] * $m[ 5];
  
    float $det = $m[0] * $inv[0] + $m[4] * $inv[1] + $m[8] * $inv[2] + $m[12] * $inv[3];
  
    if($det == 0){
        $invOut[16] = -1;
        return $invOut;
    }
  
    $det = 1.0 / $det;
  
    for($i = 0; $i < 16; $i++)
        $invOut[ $i ] = $inv[ $i ] * $det;
  
    return $invOut;
}

But if we are being serious this is how you use Python in Maya to invert a matrix:

from maya.api.OpenMaya import MMatrix
from typing import List
    
def floatToMatrix(floatList : List[float]) -> MMatrix:
    # convert list of 16 floats to an OpenMaya MMatrix    
    matrix = MMatrix()
    for i in range(16):
        matrix[i] = floatList[i]
    return matrix

def matrixToFloatList(matrix : MMatrix) -> List[float] :
    # converts MMatrix to a list of 16 floats    
    return [matrix[i] for i in range(16)]
    
    
prebindMatrix : List[float] = cmds.getAttr("%s.bindPreMatrix[%s]" % ("skinCluster25", 0))
print( prebindMatrix )
matInv : MMatrix = floatToMatrix(prebindMatrix).inverse()
print( matrixToFloatList(matInv) )

Related:

https://forums.cgsociety.org/t/mel-inverse-matrices/880267

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-- William Shakespeare, "King John"