If `A=[1 0 2 0 2 1 2 0 3]` , prove that `A^3-6A^2+7A+2I=0`

If A=[1 0 2 0 2 1 2 0 3] , then show that A is a root of the polynomial f(x)=x^3-6x^2+7x+2 .

If A=[(3, 2, 0),( 1, 4 ,0 ),(0 ,0 ,5)] , show that A^2-7A+10 I=O .

If A=[(2, 3),( 1, 2)] , verify that A^2-4A+I=O , where I=[(1, 0),( 0, 1)] and O=[(0, 0),( 0, 0)] . Hence, find A^(-1) .

If A A=[3-2 4-2] and I=[1 0 0 1] , find k so that A^2=k A-2I .

If A=[ (3,-2),( 4 ,-2) ] and I=[(1,0),(0,1)] , then prove that A^2-A+2I=O .

If A=[[3, 1],[-1, 2]] , show that A^2-5A+7I=0

If A A=[[3,-2],[ 4,-2]] and I=[[1, 0],[ 0, 1]] , find k so that A^2=k A-2I .

If A = [ (-3 , 2) , (1, -1)] and I = [(1,0) , (0, 1)] , find the scalar k so that A^2 +I = kA .

If A = [ (-3 , 2) , (1, -1)] and I = [(1,0) , (0, 1)] , find the scalar k so that A^2 +I = kA .

If A=[(1, 0,-3 ),(2, 1 ,3 ),(0, 1 ,1)] , then verify that A^2+A=A(A+I) , where I is the identity matrix.