====== Question 10, Exercise 2.2 ======
Solutions of Question 10 of Exercise 2.2 of Unit 02: Matrices and Determinants. This is unit of Model Textbook of Mathematics for Class XI published by National Book Foundation (NBF) as Federal Textbook Board, Islamabad, Pakistan. 

=====Question 10=====
If $A$ and $B$ are two matrices such that $A B=B$ and $B A=A$. Find $A^{2}+B^{2}$

** Solution. **

	
Given  $$AB = B$$ and $$BA = A$$	
\begin{align*}
A^2 &= AA\\
& = A(BA)\\
&=(AB)A\\
&=BA\\
&=A
\end{align*} 
Similarly,
\begin{align*}
B^2&= BB \\
&=B(AB)\\
& = (BA)B\\
&=AB\\
&=B\end{align*}	 
Now, $$A^2 + B^2 = A + B$$ 
Therefore, given the conditions $AB = B$ and $BA = A$, we find that:
$$A^2 + B^2 = A + B $$



====Go to ====

<text align="left"><btn type="primary">[[math-11-nbf:sol:unit02:ex2-2-p9|< Question 9]]</btn></text>
<text align="right"><btn type="success">[[math-11-nbf:sol:unit02:ex2-2-p11|Question 11 >]]</btn></text>