" If "A=[[1,0],[0,1]]" and "B=[[0,1],[-1,1]]" ,show that "(aA+bB)(aA-bB)=(a^(2)+b^(2))A

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[(-1,0),(0,1)] and B=[(0,1),(1,0)] , show that (A+B)^2 ne A^2+2AB+B^2 .

If A=[{:(0,1),(1,1):}]andB=[{:(0,-1),(1,0):}] show that (A+B)*(A-B)neA^(2)-B^(2) .

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

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

(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.

(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 = [[2,1],[3,0]] find a and b such that A^(2)+aA+bl_(2)=0 Hence, find A^(-1) .

If A = {:[(1,0),(1,1)] and A^2 = aA + bI , then (a,b)