Question

If A = \[ A = \begin{pmatrix} 0 & -3 & 8 \\ 3 & 0 & 5 \\ -8 & -5 & 0 \end{pmatrix} \] then A is a :

• A. null matrix
• B. symmetric matrix
• C. skew-symmetric matrix
• D. diagonal matrix

Hint:

A matrix is skew-symmetric if the transpose of the matrix is equal to the negative of the matrix.

Answer 1

The Correct Option is C

To determine whether the matrix $A$ is skew-symmetric, we check if $A^T = -A$. Taking the transpose of $A$: \[ A^T = \begin{pmatrix} 0 & 3 & -8 \\ -3 & 0 & -5 \\ 8 & 5 & 0 \end{pmatrix} \] Now, check if $A^T = -A$: \[ -A = \begin{pmatrix} 0 & 3 & -8 \\ -3 & 0 & -5 \\ 8 & 5 & 0 \end{pmatrix} \] Since $A^T = -A$, we conclude that $A$ is a skew-symmetric matrix.