Question

If A is a square matrix of order 3 such that $\left|A\right|=\frac{5}{2},\mathrm{then}\left|A^{-1}\right|$ = ________________.

Answer 1

Given:
A is a square matrix of order 3
|A| = $\frac{5}{2}$


As we know,
$$\begin{gathered} \left|A^{-1}\right|={\left|A\right|}^{-1} \\ \Rightarrow \left|A^{-1}\right|=\frac{1}{\left|A\right|} \\ \Rightarrow \left|A^{-1}\right|=\frac{1}{{\displaystyle \frac{5}{2}}} \\ \Rightarrow \left|A^{-1}\right|=\frac{2}{{\displaystyle 5}} \end{gathered}$$


Hence, $\left|A^{-1}\right|=\underline{\frac{2}{5}}$.