Question

The matrix which remains unchanged under transposition is known as skew symmetric matrix.

(a) False

(b) True

I got this question by my college director while I was bunking the class.

This is a very interesting question from Real Matrices: Symmetric, Skew-symmetric, Orthogonal Quadratic Form in chapter Eigen Values and Eigen Vectors of Engineering Mathematics

Answer 1

Correct choice is (a) False

Explanation: The matrix which remains unchanged under transposition is known as symmetric matrix.

For example, if we consider a symmetric matrix A = \(\begin{bmatrix} 2 & 3 & 4 \\

3 & 5 & 6\\

4 & 6 & 7 \end{bmatrix} \) and take the transpose of it, we get,

A^T = \(\begin{bmatrix}

2 & 3 & 4 \\

3 & 5 & 6 \\

4 & 6 & 7 \end{bmatrix} \)