Q90 / 160 · WBJEE 2015 · Mathematics

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

  • A
    248
  • B
    $2 \mathrm{BA}$
  • Correct answer
    C
    $A+B$
  • D
    $A B$

Solution

Given, $A B=B$ and $B A=A$ $\begin{aligned} \text { Now, } A^{2}+B^{2} &=A \cdot A+B \cdot B \\ &=A(B A)+B(A B)=(A B) A+(\ln ) \\ &=B A+A B=A+B \end{aligned}$

Hence, the correct answer is option: 'C'.

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