If A is a skew-symmetric matrix, then which of the following is always true?
If A is a skew-symmetric matrix, then which of the following is always true?
- A. aᵢⱼ = −aⱼᵢ and aᵢᵢ = 0
- B. aᵢⱼ = aⱼᵢ
- C. A² = A
- D. A is a scalar matrix
Answer: A) aᵢⱼ = −aⱼᵢ and aᵢᵢ = 0
Explanation: A skew-symmetric matrix satisfies A' = −A, meaning aᵢⱼ = −aⱼᵢ. When i = j, this gives aᵢᵢ = −aᵢᵢ, implying aᵢᵢ = 0. So all diagonal entries are zero.
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