Q159 / 270 · NDA 2019 (Phase 1) · Mathematics

If $A=\left[\begin{array}{ll}0 & 1 \\ 1 & 0\end{array}\right]$, then matrix A is/an

  • A
    Singular matrix
  • Correct answer
    B
    Involutory matrix
  • C
    Nilpotent matrix
  • D
    Idempotent matrix

Solution

$A=\left[\begin{array}{ll}1 & 0 \\ 0 & 1\end{array}\right]$ $\begin{aligned} & A^2=\left[\begin{array}{ll}1 & 0 \\ 0 & 1\end{array}\right]\left[\begin{array}{ll}1 & 0 \\ 0 & 1\end{array}\right] \\ & =\left[\begin{array}{ll}(1)(1)+(0)(0) & (1)(0)+(0)(1) \\ (0)(1)+(1)(0) & (0)(0)+(1)(1)\end{array}\right] \\ & =\left[\begin{array}{ll}1 & 0 \\ 0 & 1\end{array}\right]=\mathrm{A}\end{aligned}$ $\therefore \mathrm{It}$ is involuntary matrix.

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

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