If A - - 1 2 1- 0 1 -1- 3 -1 1 - then show thatA3 - 3A2 - A - 9I3 - 0

[ 1 amp; 2 nbsp; amp; 1; nbsp; 0 amp; 1 amp; 1; nbsp; 3 amp; 1 amp; 1 ] A^2 = A.A = [ 1 amp; 2 nbsp; amp; 1; nbsp; 0 amp; 1 amp; 1; n ...

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Inverse of a Matrix

If A = [ 1 2 ...

Question

If $A = ⎡ ⎢ ⎣ \begin{matrix} 1 & 2 & 1 0 & 1 & - 1 3 & - 1 & 1 \end{matrix} ⎤ ⎥ ⎦$ , then show that
$A^{3} - 3 A^{2} - A + 9 I_{3} = 0$

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Solution

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