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Show that the matrix `A=[[1,2,2],[2,1,2],[2,2,1]]` satisfies the equation `A^2-4A-5I_3=0` and hence find `A^(-1)`

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Show that the matrix A=[[1 ,2, 2],[ 2, 1, 2],[ 2, 2, 1]] satisfies the equation A^2-4A-5I_3=O and hence find A^(-1) .

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If A[{:(2,3),(1,2):}] satisfy the equation A^2-kA+I=0 , then find k also A^(-1) .

Show that thematrix A= [{:(,2,3),(,1,2):}] satisfies the equations A^(2)-4A+I=0 where I is 2 xx 2 identity matrix and O is 2 xx 2 zero matrix. Using the equations. Find A^(-1) .

Show that A=[(-8, 5),( 2, 4)] satisfies the equation A^2+4A-42 I=O . Hence, find A^(-1) .

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