If `A=[(1,1),(0,1)]` , show that `A^2=[(1, 2),( 0, 1)]` and `A^3=[(1 ,3 ),(0 ,1)]` .

If A=[-1 2 0-1 1 1 0 1 0] , show that A^2=A^(-1) .

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

(i) if A=[{:(1,0),(0,1):}],B=[{:(0,1),(1,0):}]and C=[{:(1,0),(0,1):}], then show that A^(2)=B^(2)=C^(2)=I_(2). (ii) if A=[{:(1,0),(1,1):}],B=[{:(2,0),(1,1):}]and C=[{:(-1,2),(3,1):}], then show that A(B+C)=AB+AC. (iii) if A=[{:(1,-1),(-1,1):}]and B=[{:(1,1),(1,1):}], then show that AB is a zero matrix.

If A=[{:(,1,1,2),(,0,2,1),(,1,0,2):}] show that A^(3)=(5A-I)(A-I)

If A=[3-3 4 2-3 4 0-1 1] , show that A^(-1)=A^3 .

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

The matrix X in the equation AX=B, such that A= [(1,3),(0,1)] and B= [(1,-1),(0,1)] is given by (A) [(1,0),(-3,1)] (B) [(1,-4),0,1)] (C) [(1,-3),(0,1)] (D) [(0,-1),(-3,1)]

If A=[[1,-1, 1],[ 2,-1, 0],[ 1, 0, 0]] , show that A^(-1)=A^2 .

If [{:(1, 1), (0,1):}]*[{:(1, 2), (0,1):}]*[{:(1, 3), (0,1):}]cdotcdotcdot[{:(1, n-1), (0,1):}] = [{:(1, 78), (0,1):}] , then the inverse of [{:(1, n), (0,1):}] is

Let A={:[(1,2,3),(0,1,0)]:}andB={:[(-1,4,3),(1,0,0)]:} Find 2A +3B.