Q109 / 180 · COMEDK 2015 · Mathematics

If $A$ and $B$ are 2 matrices such that $A B=A$ and $B A=B$, then $B^{2}$ is equal to

  • Correct answer
    A
    $B$
  • B
    $A$
  • C
    zero matrix
  • D
    1

Solution

We have, $B A=B$ $$ \begin{aligned} &\Rightarrow(B A) B=B B \Rightarrow B(A B)=B^{2} \\ &\Rightarrow B A=B^{2} \Rightarrow B=B^{2} \end{aligned} $$

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

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