First slide

Operations of matrix

Question

If $\begin{array}{l} A = [\begin{array}{rr} \cos θ & \sin θ \\ - \sin θ & \cos θ \end{array}], \end{array}$ then $A^{2} = 1$ is true for

Moderate

A

$θ = 0$
B

$θ = \frac{π}{4}$
C

$θ = \frac{π}{2}$
D

none of these

Solution

We have,
$A^{2} = [\begin{array}{rr} \cos 2 θ \sin 2 θ \\ - \sin 2 θ \cos 2 θ \end{array}]$
$A^{2} = I \Rightarrow \cos 2 θ = 1$ and $\sin 2 θ = 0 \Rightarrow θ = 0$

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