If A= [ rr & - & ], then for what value of , A is an identity mat… - Vidyadip

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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