Question

If A = ${\displaystyle \left[\begin{array}{ccc}0& 0& 1\\ 0& 1& 0\\ 1& 0& 0\end{array}\right]}$, then A^-1 = ______ 

Options

• I

• -I

• -A

• A

Answer 1

If A = ${\displaystyle \left[\begin{array}{ccc}0& 0& 1\\ 0& 1& 0\\ 1& 0& 0\end{array}\right]}$, then A^-1 = A 

Explanation:

${\displaystyle A^{-1}=\frac{1}{\left|A\right|}}$(adj A)

= ${\displaystyle \frac{1}{-1}\left[\begin{array}{ccc}0& 0& -1\\ 0& -1& 0\\ -1& 0& 0\end{array}\right]}$

= ${\displaystyle \left[\begin{array}{ccc}0& 0& 1\\ 0& 1& 0\\ 1& 0& 0\end{array}\right]}$

∴ ${\displaystyle A^{-1}=A}$