Given A = \(
\begin{bmatrix}
3 &-4 \\[0.3em]
1 & -1 \\[0.3em]
\end{bmatrix}\)

**To prove: **A - A’ is a skew-symmetric matrix.(Note: A matrix P is skew-symmetric if P’ = -P)

**Proof: **First we will find the transpose of matrix A

A' = \(
\begin{bmatrix}
3 &-1 \\[0.3em]
-4 & -1 \\[0.3em]
\end{bmatrix}\)

Let us take P = A - A

\(\Rightarrow \) P' = P

**Hence A - A’ is a skew symmetric matrix.**