If ${\text{A}}$ and ${\text{B}}$ are two matrices such that $AB = B$ and $BA = A$, then ${A^2} + {B^2}$equals.
${\text{A}}.$ ${\text{2}}AB$
${\text{B}}.$ ${\text{2}}BA$
${\text{C}}.$ $A + B$
${\text{D}}.$ $AB$
Answer
365.4k+ 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.
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.
Last updated date: 29th Sep 2023
•
Total views: 365.4k
•
Views today: 4.65k
Recently Updated Pages
What do you mean by public facilities

Difference between hardware and software

Disadvantages of Advertising

10 Advantages and Disadvantages of Plastic

What do you mean by Endemic Species

What is the Botanical Name of Dog , Cat , Turmeric , Mushroom , Palm

Trending doubts
How do you solve x2 11x + 28 0 using the quadratic class 10 maths CBSE

Fill the blanks with the suitable prepositions 1 The class 9 english CBSE

Difference between Prokaryotic cell and Eukaryotic class 11 biology CBSE

Difference Between Plant Cell and Animal Cell

Why are resources distributed unequally over the e class 7 social science CBSE

Differentiate between homogeneous and heterogeneous class 12 chemistry CBSE

Give 10 examples for herbs , shrubs , climbers , creepers

Briefly mention the contribution of TH Morgan in g class 12 biology CBSE

What is the past tense of read class 10 english CBSE
