A skew symmetric and orthogonal matrix has eigen values (3/5) + (4i/5). How can this be possible? It must have 0 or purely imaginary values. Problem 1

Question

Problem 1. It is Orthogonal and skew symmetric but eigen values aren't purely imaginary or zero

Are the following matrices symmetric, skew-symmetric and/or orthogonal? $$\frac15\begin{bmatrix}3&-4\\4&3\end{bmatrix}$$

Answer 1

This matrix is not skew-symmetric, the diagonal entries are non-zero.