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`.

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

If A= [[a,b],[c,d]] and I= [[1,0],[0,1]] then A^(2)-(a+d)A=

If A=[[i,0],[0,i]] and B=[[0,-i],[-1,0]] then (A+B)(A-B)=

If I=[[1,0],[0,1]] and E=[[0,1],[0,0]] prove that (2I+3E)^3=8I+36E

If A=[[1/3,2],[0,2x-3]] , B=[[3,6],[0,-1]] and AB=I ,then x=

If A=[[a,b],[c,d]] and I=[[1,0],[0,1]] then A^2-(a+d)A-(bc-ad)I=

If A=[[i, 0], [0, (i)/(2)]] , then A^(-1)=

(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=[(5,2),(-1,2)] and I=[(1,0),(0,1)] show that : (A-3I)(A-4I)=O