Orthonormal (orthogonal) matrices are matrices in which the columns vectors form an orthonormal set (each column vector has length one and is orthogonal to all the other colum vectors).
For square orthonormal matrices, the inverse is simply the transpose,
Q-1 = QT
This can be seen from:
It can be seen, from inverting the order of the factors, that the rows of a square orthonormal matrices are an orthonormal set too.
Complex orthogonal matrices are called ``unitary''.