Which of the following is NOT true for matrices $A,B,C$ (assuming dimensions allow operations)?

Option B is false because matrix multiplication does not follow the cancellation law unless $A$ is non-singular ($|A|\ne 0$).Option C is also false; two non-zero matrices can have a zero product (divisors of zero), e.g., $A=\left[\begin{array}{cc}0& 1\\ 0& 0\end{array}\right],B=\left[\begin{array}{cc}1& 0\\ 0& 0\end{array}\right]⟹AB=0$.(Note: Based on the provided source solution, both B and C are technically not "always" true, but C is the classic counter-example highlighted).