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Question

Assertion :If F(α)=cosαsinα0sinαcosα0001, then [F(α)]1=F(α). Reason: For matrix G(β)=cosβ0sinβ010sinβ0cosβ, 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)|=cosαsinα0sinαcosα00011=cosαsinα0sinαcosα0001=cos(α)sin(α)0sin(α)cos(α)0001=F(α)
Now
G(β)1=adjG(β)|G(β)|=cosβ0sinβ010sinβ0cosβ1 =cos(β)0sin(β)010sin(β)0cos(β) =G(β)
So Statement 1 & 2 are individually true.
But statement 2 is not the correct explanation because these answers are just question specific.

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