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Q.

Suppose A is a 3×3 skew-symmetric matrix. Let B=(I+A)−1(I−A). Then

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a

B is orthogonal

b

B is skew symmetric

c

B2 = O

d

B is a diagonal matrix

answer is A.

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Detailed Solution

We haveBB′=(I+A)−1(I−A)(I+A)−1(I−A)′=(I+A)−1(I−A)(I−A)′(I+A)′−1=(I+A)−1(I−A)(I+A)(I−A)−1∵ A′=−A=(I+A)−1(I+A)(I−A)(I−A)−1 [I+A and I-Acommute]= (I) (I) = IThus, B is orthogonal.

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