If $$A = \left[ {\matrix{ {\cos \theta } & {\sin \theta } \cr { - \sin \theta } & {\cos \theta } \cr } } \right]$$, then what is A³ equal to?

What is the order of $$\left[ {\matrix{ x & y & z \cr } } \right]\left[ {\matrix{ a & h & g \cr h & b & f \cr g & f & c \cr } } \right]\left[ {\matrix{ x \cr y \cr z \cr } } \right]$$ ?

If $$A = \left[ {\matrix{ 0 & 1 \cr 1 & 0 \cr } } \right]$$, then the value of A⁴ is

A square matrix A is called orthogonal, if

where A' is the transpose of A