First slide

Transpose of matrix

Question

If A is a 3 × 3 skew-symmetric matrix, then trace of A is

Moderate

A

$|A|$
B

1
C

-1
D

None of these

Solution

As A is a skew symmetric matrix
⇒ a_ii = 0 ∀ i ⇒ trace(A) = 0
Also, |A| = |A′| = |–A| = (–1)³|A|
⇒ 2|A| = 0 ⇒ |A| = 0
$∴$ trace(A) = |A|.

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