Home
Class 12
MATHS
If A=[1 0 0 1] , B=[1 0 0-1] and C=[0 1 ...

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=I_2` .

Promotional Banner

Similar Questions

Explore conceptually related problems

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=[[0,1],[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.

(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,-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),(1,1)], 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=[{:( 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=[{:(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)