Q161 / 270 · NDA 2012 (Phase 1) · Mathematics

A and B are two matrices such that $\mathrm{AB}=\mathrm{A}$ and $\mathrm{BA}=\mathrm{B}$ then what is $\mathrm{B}^2$ equal to? where I is the identity matrix

  • A
    B
  • Correct answer
    B
    A
  • C
    I
  • D
    -I

Solution

$\begin{aligned} & \mathrm{AB}=\mathrm{A} \\ & \mathrm{BA}=\mathrm{B} \\ & \mathrm{ABA}=\mathrm{A} .\end{aligned}$

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

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