# how many orthogonal matrices are there in the residue field?

Task: Calculate $\mid O_3(\mathbb{Z}/3\mathbb{Z})\mid$ and $\mid O_4(\mathbb{Z}/2\mathbb{Z})\mid$ where $O_n$ represents alle the $n\times n$ matrices where $A^{-1} = A^T$ so that $A \cdot A^T= I_n$ the $n \times n$ where $n \times n$ identity matrix.