5.If `A=[[i,0],[0,i]]` then find `A^2`

If A=[[i,0], [0,i]] , write A^2 .

If A= [[1 , 0],[ − 1, 7]] and I=[[1, 0],[ 0 ,1]] , then find k so that A^2=8A+k I

If A=[[3 ,1],[-1 ,2]] and I=[[1, 0],[ 0, 1]] , then find lambda so that A^2=5A+lambdaI

2.If A=[[i,0],[0,-i]] and B=[[0,i],[i,0]], find AB .

2.If A=[[i,0],[0,-i]] and B=[[0,i],[i,0]], find AB .

If A=[[0,1],[1,0]],B=[[0,-i],[i,0]] and C=[[i,0],[0,-i]] , show that A^2=B^2=-C^2=I_2 and AB=-BA,AC=-CA and BC=-CB .

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

If A=[(i,0), (0,i)],\ n in N , then A^(4n) equals [(0,i), (i,0)] (b) [(0 ,0) ,(0, 0)] (c) [(1, 0) ,(0, 1)] (d) [(0,i) ,(i,0)]

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

matrix A=({:(-i,0),(0,-i):}) then A^2 =