Correct answer: (C) If B is skew-symmetric,then A is orthogonal.
Explanation
If B is skew-symmetric,I+B is invertible and A=(I−B)(I+B)⁻¹. Transposing and using Bᵀ=−B shows AᵀA=I,proving **C**. A=0 gives B=I and refutes A. Nonzero real skew-symmetric A has nonreal eigenvalues but its Cayley transform B is orthogonal,refuting B. For skew B,the Cayley transform A has determinant +1,not −1.
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