Question

If AB=A, BA=B then find the value of $A^2+B^2=?$
A.A+B
B.A-B
C.$2{A^2}{B^2}$
D.0

Answer 1

Hint: Here the question has to solve for the given equation, where we have to square and add two given variables in the question, and the values are also provided. Here for solving this question we need to find the square of the variables.

Complete step-by-step answer:
The question need to find the value of the expression given, where we need to find the square of two variables given and then add those values in order to get the final result of the solution, here on solving we get:
Value of A=AB
Value of B=BA
Now the given expression is=\[{A^2} + {B^2}\]
Now finding the solution of the expression by putting value we get:
\[ \Rightarrow {A^2} + {B^2} = {(AB)^2} + {(BA)^2} = {A^2}{B^2} + {B^2}{A^2} = 2{A^2}{B^2}\]
Hence we got the solution for the expression.
So, the correct answer is “Option C”.

Note: Here the given question Is to find the value of the expression which consist of two variable, in order to solve theses question we can have two approaches, one is to first solve the expression with the variables and then put the values of the variable, and the other one is to solve the expression by directly putting the values of the variables.