Question

The matrix \[ \begin{pmatrix} 0 & 1 & -2 \\ -1 & 0 & -7 \\ 2 & 7 & 0 \end{pmatrix} \] is a :

• A. diagonal matrix
• B. symmetric matrix
• C. skew symmetric matrix
• D. scalar matrix

Hint:

To check for skew-symmetry, take the transpose of the matrix and check if $A^T = -A$.

Answer 1

The Correct Option is C

A matrix is defined as skew-symmetric when its transpose equals the negative of the original matrix, i.e., $A^T = -A$. We will now verify this condition for the provided matrix: \[A^T = \begin{pmatrix} 0 & -1 & 2 \\1 & 0 & 7 \\-2 & -7 & 0\end{pmatrix}\]Observing the result, we confirm that $A^T = -A$, establishing the given matrix as skew-symmetric.