First slide

Transpose of matrix

Question

If A is a 3 x 3 skew-symmetric matrix, then trace of A is equal to

Moderate

A

-1
B

1
C

$|A|$
D

0

Solution

As A is a skew-symmetric matrix
$\begin{array}{l} A^{T} = - A \\ \Rightarrow a_{ii} = 0 \forall i \\ \Rightarrow tr (A) = 0 \\ Also | A | = |A^{T}| = | - A | = (- 1)^{3} | A | \\ \Rightarrow 2 | A | = 0 \\ \Rightarrow | A | = 0 \end{array}$

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