Orthogonal matrix

A $n \times n$ matrix $\mathbf{A}$ is an orthogonal matrix if $$\mathbf{AA}^{\sf T} = I$$ where $\mathbf{A}^{\sf T}$ is the transpose of $\mathbf{A}$ and $\mathbf{I}$ is the identity matrix.

Orthogonal matrices are always invertible, $$\mathbf{A}^{-1} = \mathbf{A}^{\sf T}$$

The rows of an orthogonal matrix form an orthonormal basis.

References:

1. https://mathworld.wolfram.com/OrthogonalMatrix.html
2. https://www.ucl.ac.uk/~ucahmdl/LessonPlans/Lesson10.pdf