[" 3.Find that the matrix "A=[[2,-1,1],[-1,2,-1],[1,-1,2]]" satisfy the equation "A^(3)-6A^(2)" ."],[qquad 9A+41=0" ; Hence deduce "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) .

Find the rank of the matrix A = [[0,1,2,-2],[4,0,2,6],[2,1,3,1]]

If A = [[2,-1,1],[-1,2,-1],[1,-1,2]] , Verify that A^3-6A^2+9A-4I=O and hence 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 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)

(2) Find the rank of the matrix A=[[1,2,3,-1],[3,6,9,-3],[2,4,6,-2]]

Solve the following equations by matrix method. If A = [(2,-1,1),(-1,2,-1),(1,-1,2)] verify that A^(3) - 6A^(2) + 9A = 4 I = 0 and hence, find A^(-1) .

If A= {:[( 2,-1,1),(-1,2,-1),(1,-1,2) ]:} Verify that A^(3) -6A^(2) +9A -4I=O and hence find A^(-1)

If A= {:[( 2,-1,1),(-1,2,-1),(1,-1,2) ]:} Verify that A^(3) -6A^(2) +9A -4I=O and hence find A^(-1)