Question

If A = (a_ij)_{3 × 3} is a skew-symmetric matrix, then

(A) a_ii = 0,∀ i

(B) A - A′ is null matrix

(C) |A| ≠ 0

(D) None of these 

Answer 1

Answer is(A) a_ii = 0,∀ i

We know that [a_ij]' = - [a_ij] for skew-symmetric matrix. Then 

[a_ji] + [a_ij] = 0

⇒a_ji + a_ij = 0

For i = j, we get a_ii + a_ii = 0

⇒ a_ii = 0

This means diagonal elements of every skew-symmetric matrix are zero.