If A and B are two matrices such that AB = B, BA = A then A2 + B2 =.

Question

If A and B are two matrices such that AB = B, BA = A then A2 + B2 =. (A) 2 AB  (B) 2 BA  (C) A + B  (D)  AB

Tardigrade Admin · Accepted Answer

Given, AB = B multiply by A on both sides ABA=BA .....(i) Also, BA= A Multiply by B on both sides BAB= AB ....(ii) Adding (i) and (ii), we get ABA + BAB = BA + AB ⇒ A(BA) + B(AB) = BA + AB ⇒ AA + BB= A + B ⇒ A2+ B2 = A + B

Q. If $A$ and $B$ are two matrices such that $A B = B, B A = A$ then $A^{2} + B^{2} =$ .

$2 A B$

$2 B A$

$A + B$

$A B$

Q. If A and B are two matrices such that AB=B,BA=A then A2+B2=.

2AB

2BA

A+B

AB

Given, AB=B multiply by A on both sides ABA=BA .....(i) Also, BA=A Multiply by B on both sides BAB=AB....(ii) Adding (i) and (ii), we get ABA+BAB=BA+AB ⇒A(BA)+B(AB)=BA+AB ⇒AA+BB=A+B ⇒A2+B2=A+B

Q. If $A$ and $B$ are two matrices such that $A B = B, B A = A$ then $A^{2} + B^{2} =$ .

$2 A B$

$2 B A$

$A + B$

$A B$