Show that the matrix `A=[2 3 1 2]`satisfies the equation `A^2-4A+I=0`

Show that the matrix A=[(2, 3), (1, 2)] satisfies the equation A^3-4A^2+A=O .

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 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)

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

Show that A=|[2,-3], [3 ,4]| satisfies the equation x^2-6x+17=0 . Hence, find A^(-1) .

Show that A=[(5, 3),(-1,-2)] satisfies the equation x^2-3x-7=0 . Thus, find A^(-1)

Show that A=[(6, 5),( 7, 6)] satisfies the equation x^2-12 x+1=0 . Thus, find A^(-1)

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) .

Show that the matrix, A=[[1, 0,-2],[-2,-1, 2],[ 3, 4, 1]] satisfies the equation, A^3-A^2-3A-I_3=O . Hence, find A^(-1) .

Let A be a squarre matrix of order of order 3 satisfies the matrix equation A^(3) -6 A ^(2) + 7 A - 8 I = O and B = A- 2 I . Also, det A = 8. The value of det (adj(I-2A^(-1))) is equal to