Q250 / 270 · NDA 2012 (Phase 1) · Mathematics

If $A$ is a square matrix such that $A^2=1$ where $I$ is the identity matrix, then what is $\mathrm{A}^{-1}$ equal to?

  • A
    A+1
  • B
    Null matrix
  • Correct answer
    C
    A
  • D
    Transpose of A

Solution

$\begin{aligned} \mathrm{A}^2 & =\mathrm{I} \\ \Rightarrow \quad \mathrm{A}^2 \mathrm{~A}^{-1} & =\mathrm{IA}^{-1} \\ \mathrm{~A} & =\mathrm{A}^{-1} .\end{aligned}$

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

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