Do non unitary involutary matrices exist?

Question

Consider an involutary matrix. This means that the square of the matrix is identity. Identity is clearly a unitary matrix. However, it is not obvious that this matrix should be a unitary one. But, do nonunitary involutary matrices exist? If yes, what could be a simple example?

Answer 1

Try $$\pmatrix{t & 1\cr 1 - t^2 & -t}$$

Answer 2

The example I often use is $\pmatrix{1&t\\ 0&-1}$ for any $t\ne0$.