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NDA 2019
Exam
NDA
Year
2019
Subject
Mathematics
Chapter
Matrices

NDA 2019 · Mathematics · Matrices

If A=[ array ll 0 & 1 1 & 0 array ] , then matrix A is/an

If A=\left[0110\begin{array}{ll}0 & 1 \\ 1 & 0\end{array}\right], then matrix A is/an

Options

  1. ASingular matrix
  2. BInvolutory matrix
  3. CNilpotent matrix
  4. DIdempotent matrix

Correct answer

B. Involutory matrix

Step-by-step solution

A=\left[1001\begin{array}{ll}1 & 0 \\ 0 & 1\end{array}\right]A2=[1001][1001]=[(1)(1)+(0)(0)(1)(0)+(0)(1)(0)(1)+(1)(0)(0)(0)+(1)(1)]=[1001]=A\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}∴It\therefore \mathrm{It} is involuntary matrix.
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