Show that the matrix A = [(0,a,b)(-a,0,c)(-b,-c,0)] is skew-symmetric.

Question

Show that the matrix A = \( \begin{bmatrix} 0 &a & b \\[0.3em] -a & 0 & c\\[0.3em] -b & -c& 0 \end{bmatrix}\)is skew-symmetric.

A = [(0,a,b)(-a,0,c)(-b,-c,0)]

HINT: Show that A’ = -A.

Answer 1

Given A = \( \begin{bmatrix} 0 &a & b \\[0.3em] -a & 0 & c\\[0.3em] -b & -c& 0 \end{bmatrix}\)

To Prove: A is a skew symmetric matrix.

Proof: As for a matrix to be skew symmetric A’ = -A

We will find A’.

\(\Rightarrow\) A' = -A

So A is A skew symmetric matrix.