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BITSAT 2014
Exam
BITSAT
Year
2014
Subject
Mathematics
Chapter
Matrices

BITSAT 2014 · Mathematics · Matrices

If [ array cc α & β γ & -α array ] is square root of identity...

If \left[αβγ−α\begin{array}{cc}\alpha & \beta \\ \gamma & -\alpha\end{array}$\right] is square root of identity matrix of order 2 then -$

Options

  1. A1+α2+βγ=01+\alpha^{2}+\beta \gamma=0
  2. B1+α2−βγ=01+\alpha^{2}-\beta \gamma=0
  3. C1−α2+βγ=01-\alpha^{2}+\beta \gamma=0
  4. Dα2+βγ=1\alpha^{2}+\beta \gamma=1

Correct answer

D. α2+βγ=1\alpha^{2}+\beta \gamma=1

Step-by-step solution

\left[αβγ−α\begin{array}{cc}\alpha & \beta \\ \gamma & -\alpha\end{array}\right]=\sqrt{\mathrm{I}_{2}}; \left[αβγ−α\begin{array}{lc}\alpha & \beta \\ \gamma & -\alpha\end{array}\right]\left[αβγ−α\begin{array}{cc}\alpha & \beta \\ \gamma & -\alpha\end{array}\right]=\left[1001\begin{array}{cc}1 & 0 \\ 0 & 1\end{array}\right]\Rightarrow \alpha^{2}+\beta \gamma=1
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