Question

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

• A. $detA$
• B. $\frac{1}{detA}$
• C. $1$
• D. None of the above

Answer 1

The correct option is B $\frac{1}{detA}$

We know

$A{A}^{-1}=I$

$\Rightarrow \left|A{A}^{-1}\right|=\left|I\right|$

$\Rightarrow \left|A\right|\left|A^{-1}\right|=1$

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

$\Rightarrow \left|A^{-1}\right|={\left|A\right|}^{-1}$

Option B