If A is an invertible matrix,

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 $A,\left|A^{-1}\right|=\frac{1}{|A|}$.

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