Is there anything special about this matrix? I've just encountered a matrix which seems to display nothing special to me:
$$B=\begin{pmatrix}1&4&2\\0 &-3 &-2\\ 0 &4 &3 \end{pmatrix}$$
But further observation reveals something stunning:
$$B^n=\cases{{I}&n is even\\{B}&n is odd}$$
So it leads me to wonder if there is indeed some special properties of this matrix $B$, or more probably, $B$ belongs to a whole special class of matrices whose name I don't know? Could you drop me a hint? Thanks in advance.

EDIT I think I was being a bit stupid... It suddenly hit me that any matrix $B$ such that $B^2=I$ will have this property.

$B$ is a square root of unity. See http://en.wikipedia.org/wiki/Square_root_of_a_matrix for more about square roots of matrices.
