If `A=[1 2 2 2 1 2 2 2 1]` , then prove that `A^2-4A-5I=O` .

If A=[1 2 2 2 1 2 2 2 1] , then show that A^2-4A-5I=O ,w h e r eIa n d0 are the unit matrix and the null matrix of order 3, respectively. Use this result to find A^(-1)dot

If A=[1 2 2 2 1 2 2 2 1] , find A^(-1) and prove that A^2-4A-5I=O .

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

If A=[{:(1,2,2),(2,1,2),(2,2,1):}] , then show that A^(2)-4A-5I_(3)=0 . Hemce find A^(-1) .

(i) if A=[{:(1,-1),(2,3):}], then show that A^(2)-4A+5I=O. (ii) if f(x)=x^(2)+3x-5and A=[{:(2,-1),(4,3):}], then find f(A).

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) .

If A=[[4, 2],[-1, 1]] , prove that (A-2I)(A-3I)=O .

If A^(3)=O , then prove that (I-A)^(-1) =I+A+A^(2) .

If (a+ib)= (1+i ) /(1-i) , then prove that (a ^2+b^ 2 )=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) .