Question

If A is an invertible matrix, then det $\left(A^{-1}\right)$ is equal to

• A. $det\left(A\right)$
• B. $\frac{1}{det\left(A\right)}$
• C. $1$
• D. none of these

Answer 1

The correct option is B $\frac{1}{det\left(A\right)}$

We know that $|A^n|=|A{|}^n$ n be any integer
$\Rightarrow |A^{-1}|=|A{|}^{-1}=\frac{1}{|A|}$