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If $A = (\begin{array}{cc} \cos θ & - \sin θ \\ \sin θ & \cos θ \end{array})$ , then

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a

A is an orthogonal matrix

b

A is a symmetric matrix

c

A is a skew-symmetric matrix

d

none of these

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detailed solution

Correct option is A

We haveAA′=cos⁡θ−sin⁡θsin⁡θcos⁡θcos⁡θsin⁡θ−sin⁡θcos⁡θ=cos2⁡θ+sin2⁡θcos⁡θsin⁡θ−sin⁡θcos⁡θcos⁡θsin⁡θ−sin⁡θcos⁡θsin2⁡θ+cos2⁡θ=1 00 1=I2Similarly, A′A=I2Thus, A is an orthogonal matrix.

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