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Matrices — Maths STD 12 Science — Question

Gujarat BoardEnglish MediumSTD 12 ScienceMathsMatrices1 Mark
MCQ
If $A=\left[\begin{array}{rr}\cos \alpha & -\sin \alpha \\ \sin \alpha & \cos \alpha\end{array}\right]$, then for what value of $\alpha, A$ is an identity matrix?
  • ✓
    $0^{\circ}$
  • B
    $90^{\circ}$
  • C
    $45^{\circ}$
  • D
    $30^{\circ}$
✓

Answer

Correct option: A.
$0^{\circ}$
(a) : $A=\left[\begin{array}{rr}\cos \alpha & -\sin \alpha \\ \sin \alpha & \cos \alpha\end{array}\right]$ is an identity matrix if, $\left[\begin{array}{rr}\cos \alpha & -\sin \alpha \\ \sin \alpha & \cos \alpha\end{array}\right]=\left[\begin{array}{ll}1 & 0 \\ 0 & 1\end{array}\right]$
$\therefore \cos \alpha=1$ and $\sin \alpha=0 \Rightarrow \alpha=0^{\circ}$.

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