True or false. If the determinant of AB is zero, then the determinant of A is zero or the determinant of B is zero.
I put true in my exam. After all det(A)det(B)=det(AB).
Why was I wrong? The answer is apparently is wrong.
2026-04-03 03:21:49.1775186509
Det(AB)=0: what is the determinant of A and B
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It is possible for $AB$ to be a square matrix but neither of $A$ nor $B$ is square, for example if $A$ is a $2 \times 3$ matrix and $B$ is a $3 \times 2$ matrix. In this case, it is possible that $\det(AB)$ will be zero, but the determinants of $A$ and $B$ are not defined.
It may be that this is why your answer was marked as incorrect. However, if it was specified that $A$ and $B$ be square, then your answer was correct (and so was your reasoning).