Hi I was wondering if we have 2 for example A,B matrix 2x2 with integers and DetA≠0 , DetB≠0 the 2x2 Matrix \(C=A\times B\) will have DetC≠0?

There is a theorem of this and a proof?

As follows:

Determinant of the multiplication is always the multiplication of the determinants for any 2 square matrices

Also welcome back dimitris