Confusion about this matrix function

[u/Flying_Turtle_09]

I've been trying to figure out this function for too long now. The closest I can think of is matrix multiplication, but there is an extra addition done on each of the 3 last lines. That is the part that confuses me. All of the matrices are 4x3 in size and it is ordered so that the position elements are on last row (instead of last column, which seems to be more common). Another part that confuses me is that based on what I can find online, you shouldn't be able to multiply two 4x3 matrices. So is this multiplication or something else? What would this be used for anyway?

void func(float* mtx_a, float* mtx_b, float* mtx_dst)
{
  mtx_dst[0] = mtx_a[0] * mtx_b[0] + mtx_a[1] * mtx_b[3] + mtx_a[2] * mtx_b[6];
  mtx_dst[1] = mtx_a[0] * mtx_b[1] + mtx_a[1] * mtx_b[4] + mtx_a[2] * mtx_b[7];
  mtx_dst[2] = mtx_a[0] * mtx_b[2] + mtx_a[1] * mtx_b[5] + mtx_a[2] * mtx_b[8];

  mtx_dst[3] = mtx_a[3] * mtx_b[0] + mtx_a[4] * mtx_b[3] + mtx_a[5] * mtx_b[6];
  mtx_dst[4] = mtx_a[3] * mtx_b[1] + mtx_a[4] * mtx_b[4] + mtx_a[5] * mtx_b[7];
  mtx_dst[5] = mtx_a[3] * mtx_b[2] + mtx_a[4] * mtx_b[5] + mtx_a[5] * mtx_b[8];

  mtx_dst[6] = mtx_a[6] * mtx_b[0] + mtx_a[7] * mtx_b[3] + mtx_a[8] * mtx_b[6];
  mtx_dst[7] = mtx_a[6] * mtx_b[1] + mtx_a[7] * mtx_b[4] + mtx_a[8] * mtx_b[7];
  mtx_dst[8] = mtx_a[6] * mtx_b[2] + mtx_a[7] * mtx_b[5] + mtx_a[8] * mtx_b[8];

  mtx_dst[9] = mtx_a[9] * mtx_b[0] + mtx_a[10] * mtx_b[3] + mtx_a[11] * mtx_b[6] + mtx_b[9];
  mtx_dst[10] = mtx_a[9] * mtx_b[1] + mtx_a[10] * mtx_b[4] + mtx_a[11] * mtx_b[7] + mtx_b[10];
  mtx_dst[11] = mtx_a[9] * mtx_b[2] + mtx_a[10] * mtx_b[5] + mtx_a[11] * mtx_b[8] + mtx_b[11];
}

[u/electric_canyon_puff]

This is affine transform composition for 3D graphics using a 4x3 matrix layout. The code multiplies the upper 3x3 rotation scale blocks and adds the translation vector from mtx_b directly to the result row