Question

If A=\(\begin{bmatrix}1&0\\0&1\end{bmatrix}\), then which of the following statement is incorrect?

(a) A is a skew-symmetric matrix

(b) A is a square matrix

(c) A is a symmetric

(d) A is an identity matrix

This question was posed to me in my homework.

I want to ask this question from Symmetric and Skew Symmetric Matrices topic in division Matrices of Mathematics – Class 12

Answer 1

The correct option is (a) A is a skew-symmetric matrix

To explain: Given that, A=\(\begin{bmatrix}1&0\\0&1\end{bmatrix}\)

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

⇒-A’=\(\begin{bmatrix}-1&0\\0&-1\end{bmatrix}\)≠A. Hence, it is not a skew symmetric matrix.