Question

If A= $\left[\begin{array}{ccc}1& 2& 2\\ 2& 1& 2\\ 2& 2& 1\end{array}\right]$   and A^-1 exists and A≠0 , then (A² -4A)A^-1= 

 

$$\begin{gathered} A)\left[\begin{array}{ccc}-3& 2& 2\\ 2& -3& 2\\ 2& 2& -3\end{array}\right] \\ B)\left[\begin{array}{ccc}3& 2& 2\\ 2& 3& 2\\ 2& 2& 3\end{array}\right] \\ C)\left[\begin{array}{ccc}5& 2& 0\\ 2& 5& 0\\ 0& 2& 5\end{array}\right] \\ D)\left[\begin{array}{ccc}5& 2& 5\\ 2& 5& 5\\ 5& 5& 2\end{array}\right] \end{gathered}$$

Answer 1

The correct answer is option a) $\left[\begin{array}{ccc}-3& 2& 2\\ 2& -3& 2\\ 2& 2& -3\end{array}\right]$

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