A square matrix $A$ satisfies $A^T A = I$. Such a matrix is called:

An orthogonal matrix satisfies $A^T A = A A^T = I$, equivalently $A^{-1} = A^T$. Its rows (and columns) form an orthonormal set. Rotation and reflection matrices in $\mathbb{R}^n$ are orthogonal. $|A|$ for an orthogonal matrix is always $\pm 1$.