If $$A=$$$$cos$$⁡θ −$$sin$$⁡θ$$sin$$⁡θ $$cos$$⁡θ ,then $$AT+A=I2$$ if

Correct option is 3θ=2nπ+π3,n∈Z

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If $A = [\begin{array}{rr} \cos θ - \sin θ \\ \sin θ \cos θ \end{array}]$ ,then $A^{T} + A = I_{2}$ if

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θ=nπ,n∈Z

θ=(2n+1)π2,n∈Z

θ=2nπ+π3,n∈Z

None of these

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detailed solution

Correct option is C

We have, AT+A=I2⇒ cos⁡θsin⁡θ−sin⁡θcos⁡θ+cos⁡θ−sin⁡θsin⁡θcos⁡θ=1001⇒ 2cos⁡θ002cos⁡θ=1001⇒ cos⁡θ=12=cos⁡π3⇒θ=2nπ±π3,n∈Z

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If A=cos⁡θ −sin⁡θsin⁡θ cos⁡θ ,then AT+A=I2 if

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If $A = [\begin{array}{rr} \cos θ - \sin θ \\ \sin θ \cos θ \end{array}]$ ,then $A^{T} + A = I_{2}$ if