Question

Which of the following matrix is Skew Symmetric?

(a) \(\begin{bmatrix}0&1\\-1&0\end{bmatrix}\)

(b) \(\begin{bmatrix}0&1\\1&0\end{bmatrix}\)

(c) \(\begin{bmatrix}0&3\\-1&9\end{bmatrix}\)

(d) \(\begin{bmatrix}8&-2\\-1&3\end{bmatrix}\)

I had been asked this question during a job interview.

My enquiry is from Types and Properties of Matrices in section Matrices of Engineering Mathematics

Answer 1

Right option is (a) \(\begin{bmatrix}0&1\\-1&0\end{bmatrix}\)

Easy explanation: We know for a Skew Symmetric Matrix,

A=-A^T

So for option \(\begin{bmatrix}0&1\\-1&0\end{bmatrix}\),

A^T=\(\begin{bmatrix}0&-1\\1&0\end{bmatrix}\)=(-1)\(\begin{bmatrix}0&1\\-1&0\end{bmatrix}\)=A.