Find A^{2}-5 A+6 I if A=left[begin{array}{ccc | vedclass

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(N/A) We have $A^{2}=A 	imes A$.$A^{2}=\left[\begin{array}{ccc}2 & 0 & 1 \ 2 & 1 & 3 \ 1 & -1 & 0\end{array}ight]\left[\begin{array}{ccc}2 & 0 &

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(N/A) We have $A^{2}=A 	imes A$.$A^{2}=\left[\begin{array}{ccc}2 & 0 & 1 \ 2 & 1 & 3 \ 1 & -1 & 0\end{array}ight]\left[\begin{array}{ccc}2 & 0 & 1 \ 2 & 1 & 3 \ 1 & -1 & 0\end{array}ight]$$A^{2}=\left[\begin{array}{ccc}2(2)+0(2)+1(1) & 2(0)+0(1)+1(-1) & 2(1)+0(3)+1(0) \ 2(2)+1(2)+3(1) & 2(0)+1(1)+3(-1) & 2(1)+1(3)+3(0) \ 1(2)+(-1)(2)+0(1) & 1(0)+(-1)(1)+0(-1) & 1(1)+(-1)(3)+0(0)\end{array}ight]$$A^{2}=\left[\begin{array}{ccc}4+0+1 & 0+0-1 & 2+0+0 \ 4+2+3 & 0+1-3 & 2+3+0 \ 2-2+0 & 0-1+0 & 1-3+0\end{array}ight] = \left[\begin{array}{ccc}5 & -1 & 2 \ 9 & -2 & 5 \ 0 & -1 & -2\end{array}ight]$Now,substitute the matrices into the expression $A^{2}-5 A+6 I$:$= \left[\begin{array}{ccc}5 & -1 & 2 \ 9 & -2 & 5 \ 0 & -1 & -2\end{array}ight] - 5\left[\begin{array}{ccc}2 & 0 & 1 \ 2 & 1 & 3 \ 1 & -1 & 0\end{array}ight] + 6\left[\begin{array}{ccc}1 & 0 & 0 \ 0 & 1 & 0 \ 0 & 0 & 1\end{array}ight]$$= \left[\begin{array}{ccc}5 & -1 & 2 \ 9 & -2 & 5 \ 0 & -1 & -2\end{array}ight] - \left[\begin{array}{ccc}10 & 0 & 5 \ 10 & 5 & 15 \ 5 & -5 & 0\end{array}ight] + \left[\begin{array}{ccc}6 & 0 & 0 \ 0 & 6 & 0 \ 0 & 0 & 6\end{array}ight]$$= \left[\begin{array}{ccc}5-10+6 & -1-0+0 & 2-5+0 \ 9-10+0 & -2-5+6 & 5-15+0 \ 0-5+0 & -1+5+0 & -2-0+6\end{array}ight]$$= \left[\begin{array}{ccc}1 & -1 & -3 \ -1 & -1 & -10 \ -5 & 4 & 4\end{array}ight]$

Find $A^{2}-5 A+6 I$ if $A=\left[\begin{array}{ccc}2 & 0 & 1 \\ 2 & 1 & 3 \\ 1 & -1 & 0\end{array}\right]$

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