If `A=[[2,-1],[-1, 2]]` and `I` is the identity matrix of order 2, then show that `A^2=4A-3I` Hence find `A^(-1)`.

If M=[{:(,1,2),(,2,1):}] and I is a unit matrix of the same order as that of M, show that M^2=2M+3I

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

If A=[(3, 1),( 1, 2)] , show that A^2-5A+5I=0 . Hence, find A^(-1) .

For the matrix A=[1 1 1 1 2-3 2-1 3] . Show that A^3-6A^2+5A+11\ I_3=O . Hence, find A^(-1) .

If A=[(2,-3),(3,4)], show the A^2-6A+17I=0. Hence find A^-1

If A=[{:(1,-1),(2,3):}] , shown that A^(2)-4A+5I=o . Hence Find A^(-1) .

Given A=[(x, 3),(y, 3)] If A^(2)=3I , where I is the identity matrix of order 2, find x and y.

For the matrix A=[{:(,3,2),(,1,1):}] Find a & b so that A^(2)+aA+bI=0 . Hence find A^(-1)

Column I, Column II If A is an idempotent matrix and I is an identity matrix of the same order, then the value of n , such that (A+I)^n=I+127 is, p. 9 If (I-A)^(-1)=I+A+A^2++A^2, then A^n=O , where n is, q. 10 If A is matrix such that a_(i j)-(i+j)(i-j),t h e nA is singular if order of matrix is, r. 7 If a non-singular matrix A is symmetric, show that A^(-1) . is also symmetric, then order A can be, s. 8