Explain why the notation A/B is ambiguous when A and B are matrices,even if det B isnot equal to 0.
I disagree with BobP. "Dividing", in any group, field, or ring, means multiplying by the inverse and is defined in a vector field.
The "ambiguity" is in A/B, and the reason "multiplying by the inverse" is never written that way, is that multiplication of matrices is not commutative. That could mean either $\displaystyle AB^{-1}$ or $\displaystyle B^{-1}A$.