15. Matrix by matrix multiplication

• We can also multiply a matrix by another matrix.

• The multiplication of two 3x3 matrices forms a 3x3 matrix, calculated as follows:

   

  The multiplication of two 4x4 matrices forms a 4x4 matrix, calculated as follows:

   

  Note: matrix order matters! We multiply them left to right, otherwise the results are drastically different:

  • AB ≠ BA

  • Av ≠ vA