Assertion :If F(α)=⎡⎢⎣cosα−sinα0sinαcosα0001⎤⎥⎦, then [F(α)]−1=F(−α). Reason: For matrix G(β)=⎡⎢⎣cosβ0sinβ010−sinβ0cosβ⎤⎥⎦, we have [G(β)]−1=G(−β)
A
Both Assertion and Reason are correct and Reason is the correct explanation for Assertion
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B
Both Assertion and Reason are correct but Reason is not the correct explanation for Assertion
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C
Assertion is correct but Reason is incorrect
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D
Assertion is incorrect but Reason is correct
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Solution
The correct option is B Both Assertion and Reason are correct but Reason is not the correct explanation for Assertion F(α)−1=adjF(α)|F(α)|=⎡⎢⎣cosαsinα0−sinαcosα0001⎤⎥⎦1=⎡⎢⎣cosαsinα0−sinαcosα0001⎤⎥⎦=⎡⎢⎣cos(−α)−sin(−α)0sin(−α)cos(−α)0001⎤⎥⎦=F(−α)