Question:
If $A$ is an invertible matrix, then $\operatorname{det}\left(A^{-1}\right)$ is equal to
(a) det $(A)$
(b) $\frac{1}{\operatorname{det}(A)}$
(c) 1
(d) none of these
Solution:
(b) $\frac{1}{\operatorname{det}(A)}$
We know that for any invertible matrix $A,\left|A^{-1}\right|=\frac{1}{|A|}$.