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

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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)]

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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.