Question

If $A$ is square matrix $A\text{'}$ is its transpose, then $\frac{1}{2}(A–A\text{'})$ is

• A. a symmetric matrix
• B. a skew – symmetric matrix
• C. a unit matrix
• D. an elementary matrix

Answer 1

The correct option is B

a skew – symmetric matrix

Explanation for the correct option:

Finding the type of matrix:

Given, $A$ is square matrix. That means,

$\begin{array}{rcl}\frac{1}{2}(A–A\text{'})& =& \frac{1}{2}(A–A\text{'})\text{'}\\ & =& \frac{1}{2}(A\text{'}–A)[{\mathbf{(}\mathbf{A}\mathbf{\text{'}}\mathbf{)}}^{\mathbf{\text{'}}}\mathbf{=}\mathbf{}\mathit{A}]\\ & =& -\frac{1}{2}(A–A\text{'})\end{array}$

$\therefore$It is a skew-symmetric matrix.

Hence, Option ‘B’ is Correct.