Not always possible. For, consider C as invertible, then by associative properly, B(AC)=(BA)C. Since (AB)C=B(AC)=(BA)C, we get (AB)C=(BA)C implies AB=BA. It implies that A and B are commutative, but in general matrix multiplication is not commutative.

If A and B are commutative, there is a chance.

Thanks a lot Panchatcharam Mariappan

Thanks a lot F. O. Farid

Not always possible. If the inverse of A is B then there is a chance such that (AB)C=A(BC)=B(AC) .

Dear Muhammad,

In addition to the helpful answers, in general,

if one needs to show any conjecture is wrong, it is enough to give a counterexample.

Best regards