Question

Which among the following is a Skew-symmetric matrix?
1. \(\begin{bmatrix} 0 & 4 & 6\\ -4 & 0 & -2 \\ -6 & 2 & 0 \end{bmatrix}\)
2. \(\begin{bmatrix} 0 &1 \\ -1& 0\end{bmatrix}\)
3. Both A & B
4. None of these

Answer 1

Correct Answer - Option 3 : Both A & B

Concept:

Square matrix A is said to be skew-symmetric if a_ij = −a_ij for all i and j.

Square matrix A is said to be skew-symmetric if the transpose of matrix A is equal to the negative of matrix A ⇔ A^T = −A

All the main diagonal elements in the skew-symmetric matrix are zero.

Calculation:

For a skew-symmetric matrix, diagonal elements are zero and AT = −A

So, both \(\begin{bmatrix} 0 & 4 & 6\\ -4 & 0 & -2 \\ -6 & 2 & 0 \end{bmatrix}\)and \(\begin{bmatrix} 0 &1 \\ -1& 0\end{bmatrix}\)are Skew-symmetric matrix.