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=[[0,1],[1,0],[0,1]] and B=[[0,1,2],[2,1,0]], find AB

If A=[[1,0,0],[0,1,0],[a,b,-1]] , find A^2

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 .

(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=[{:(0,1),(1,1):}] "and" B=[{:(0,-1),(1,0):}] , then show that (A+B)(A-B)neA^(2)-B^(2)

If A=[[0,0,1],[0,1,0],[1,0,0]],B=[[0,5,7],[0,0,6],[0,0,0]] and C=[[-1,3,5],[1,-3,-5],[-1,3,5]] , show that C^2=C

If A=[(1,0),(1,1)], B=[(2,0),(1,1)] and C=[(-1,2),(3,1)], show that

If A=[{:( 0,-x),(x,0):}].B=[{:(0,1),(1,0):}] and x^(2)=-1 , then show that (A+B)^(2)=A^(2)+B^(2) .

If A=[[1,0,1],[0,2,0],[1,-1,4]],A=B+C,B=B^(T) and C=-C^(T) , then C=

if A=[(1,2),(3,4):}],B=[{:(-1,0),(2,3):}]and C=[{:(1,-1),(0,1):}], then show that : (i) A(B+C)=AB+AC (ii) (A-B)C=AC-BC.