If A = [[a, b], [c, d]] and A' = −A, then which of the following must be true?

If A = [[a, b], [c, d]] and A' = −A, then which of the following must be true?

• A. a = d = 0 and c = −b
• B. a = b = c = d = 0
• C. a = d and b = c
• D. a = −d and b = c

Answer: A) a = d = 0 and c = −b

Explanation: A' = −A means [[a, c], [b, d]] = [[−a, −b], [−c, −d]]. Equating: a = −a → a = 0; d = −d → d = 0; c = −b; b = −c which is consistent with c = −b.