Question

If A = (\begin{bmatrix} 2 & 3 \[0.3em]4 &5 \[0.3em] \end{bmatrix}), prove that A - AT is a skew-symmetric matrix.

Answer 1

Considering

From (i) and (ii) clearly

Skew-symmetric matrix is a square matrix whose transpose equal to its negative, that is,

X = – XT

Therefore, A – AT is a skew-symmetric.