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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