If `A=[[1,0],[0,1]]` then show that `A^2=I`

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

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

If I=[[1,0],[0,1]] , then I^4=

(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=[[1,0],[0,1]],B=[[1,0],[0,-1]] and C=[[0,1],[1,0]] then show that A^(2)=B^(2)=C^(2)

If A=[[1,2,1] , [1,-4,1] , [3,0,-3]], B=[[2,1,1] , [1,-1,0] , [2,1,-1]] then show that AB=6I_3

If A=[[1,0,1],[0,1,2],[0,0,4]] then show that |3A|=27|A|

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

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