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

MCQ

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:

A
Diagonal matrix.
B
Symmetric matrix.
✓
Skew-symmetric matrix.
D
Scalar matrix.

✓

Answer

Correct option: C.

Skew-symmetric matrix.

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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