Q2Mathematics II

In matrix algebra, a real square matrix $A$ of order $n$ is explicitly termed 'orthogonal' if and only if multiplying it by its transpose strictly yields the Identity matrix $I$.

This absolute condition mathematically implies that $A^{-1}=A^T$. Furthermore, the column (and row) vectors of an orthogonal matrix form a perfectly orthonormal basis, meaning they are all mutually perpendicular exactly with a magnitude of 1. The determinant of any orthogonal matrix is rigidly restricted to exactly $+1$ (representing a pure rotation) or $-1$ (representing a reflection).