Choose the correct answer from the given four options. The matrix… - Vidyadip

Question

Choose the correct answer from the given four options.
The matrix $\begin{bmatrix}0&-5&8\\5&0&12\\-8&-12&0\end{bmatrix}$ is a:

Diagonal matrix.
Symmetric matrix.
Skew-symmetric matrix.
Scalar matrix.

✓

Answer

Skew-symmetric matrix.

Solution:
We have $\text{B}=\begin{bmatrix}0&-5&8\\5&0&12\\-8&-12&0\end{bmatrix}$
$\Rightarrow\ \text{B}'=\begin{bmatrix}0&5&8\\-5&0&-12\\8&12&0\end{bmatrix}$
$=-\begin{bmatrix}0&-5&8\\5&0&12\\-8&-12&0\end{bmatrix}$
$=-\text{B}$
Since, B' = -B,
Thus, B is a skew-symmetric matrix.

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