Question:
If $A$ is a square matrix of order 3 such that $|A|=\frac{5}{2}$, then $\left|A^{-1}\right|=$___________
Solution:
Given:
$A$ is a square matrix of order 3
$|A|=\frac{5}{2}$
As we know,
$\left|A^{-1}\right|=|A|^{-1}$
$\Rightarrow\left|A^{-1}\right|=\frac{1}{|A|}$
$\Rightarrow\left|A^{-1}\right|=\frac{1}{\frac{5}{2}}$
$\Rightarrow\left|A^{-1}\right|=\frac{2}{5}$
Hence, $\left|A^{-1}\right|=\underline{\frac{2}{5}}$.