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Question
\[A = \begin{bmatrix}2 & - 3 & - 5 \\ - 1 & 4 & 5 \\ 1 & - 3 & - 4\end{bmatrix}\] , Show that A2 = A.
Solution
Here,
`A^2`=AA
`⇒ A^2= [[2 -3 -5],[-1 4 5],[1 -3 -4]]` `[[2 -3 -5],[-1 4 5],[1 -3 -4]]`
`⇒ A^2=[[4+3-5 -6-12+15 -10-15+20],[-2-4+5 3+16-15 5+20-20],[2+3-4 -3-12+12 -5-15+16]]`
`⇒ A^2=[[2 -3 -5],[-1 4 5],[1 -3 -4]]`
∴` A^2` =A
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