If A=⎡⎢⎣122212221⎤⎥⎦, then show that A2−4A−5I=0, and – InterviewSolution

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1.	If A=⎡⎢⎣122212221⎤⎥⎦, then show that A2−4A−5I=0, and hence find A−1.
Answer» If $A = ⎡ ⎢ ⎣ \begin{matrix} 1 & 2 & 2 2 & 1 & 2 2 & 2 & 1 \end{matrix} ⎤ ⎥ ⎦$ , then show that $A^{2} - 4 A - 5 I = 0$ , and hence find $A^{- 1}$ .

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