Question

If a square matrix B is skew symmetric then.

(a) B^T = -B

(b) B^T = B

(c) B^-1 = B

(d) B^-1 = B^T

The question was asked in examination.

I need to ask this question from Basics of Linear Algebra topic in portion Linear Algebra Overview of Signals and Systems

Answer 1

The correct answer is (a) B^T = -B

The explanation: The transpose of a skew symmetric matrix should be equal to the negative of the matrix

Example: let us consider a matrix B = \(\begin{bmatrix}

a & e & d\\

-e & b & f\\

-d & -f & c\\

\end{bmatrix}\), B^T = \(\begin{bmatrix}

a & -e & -d\\

e & b & -f\\

d & f & c\\

\end{bmatrix}\).