Question

The matrix A=\(\begin{bmatrix}0&1&-1\\-1&0&1\\1&-1&0\end{bmatrix}\) is __________

(a) scalar matrix

(b) identity matrix

(c) symmetric matrix

(d) skew-symmetric matrix

I have been asked this question in unit test.

The above asked question is from Symmetric and Skew Symmetric Matrices topic in chapter Matrices of Mathematics – Class 12

Answer 1

Correct answer is (d) skew-symmetric matrix

To explain: The given matrix A=\(\begin{bmatrix}0&1&-1\\-1&0&1\\1&-1&0\end{bmatrix}\) is skew symmetric.

⇒A’=\(\begin{bmatrix}0&-1&1\\1&0&-1\\-1&1&0\end{bmatrix}\)=A

∴A=-A’. Hence, it is a skew-symmetric matrix.