If A = [(3,-4)(1,-1)] , show that (A + A’) is skew-symmetric.

Question

If A = \( \begin{bmatrix} 3& -4 \\[0.3em] 1 & -1 \\[0.3em] \end{bmatrix}\) , show that (A + A’) is skew-symmetric.

A = [(3,-4)(1,-1)]

Answer 1

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.