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Question
If \[A = \begin{bmatrix}4 & - 1 & - 4 \\ 3 & 0 & - 4 \\ 3 & - 1 & - 3\end{bmatrix}\] , Show that A2 = I3.
Solution
Here,
`A^2`=AA
⇒` A^2 =[[4 -1 -4],[3 0 -4],[3 -1 -3]]` `[[4 -1 -4],[3 0 -4],[3 -1 -3]]`
`⇒ A^2=[[16-3-12 -4+0+4 -16+4+12],[12+0-12 -3+0+4 -12+0+12],[12-3-9 -3+0+3 -12+4+9]]`
`⇒ A^2=` `[[1 0 0],[0 1 0],[0 0 1]]`
∴ `A^2=I_3`
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