Courses
Courses for Kids
Free study material
Free LIVE classes
More

If ${\text{A}}$ and ${\text{B}}$ are two matrices such that $AB = B$ and $BA = A$, then ${A^2} + {B^2}$equals.
${\text{A}}.$ ${\text{2}}AB$
${\text{B}}.$ ${\text{2}}BA$
${\text{C}}.$ $A + B$
${\text{D}}.$ $AB$

Last updated date: 21st Mar 2023
Total views: 308.1k
Views today: 6.86k
Answer
VerifiedVerified
308.1k+ views
Hint:-Here, we go through by writing ${A^2} = A.A$ and ${B^2} = B.B$ then rearrange it.

We have to find ${A^2} + {B^2}$
Given, $AB = B$ and $BA = A$
$ \Rightarrow {A^2} = A.A = A\left( {BA} \right) = \left( {AB} \right)A = BA = A$
$ \Rightarrow {B^2} = B.B = B.\left( {AB} \right) = \left( {BA} \right)B = AB = B$
$ \Rightarrow {A^2} + {B^2} = A + B$
So, option ${\text{C}}$ is the correct answer.

Note:-Whenever we face such a type of question of matrix the key concept for solving the question is you have to proceed according to what is given in question, and try to rearrange the terms to get an answer.