Orthogonal Matrix

Orthogonal Matrix is a square matrix whose columns (and rows) form an Orthonormal Basis Set: every column has length 1 and is perpendicular to every other column.

Multiplying an orthogonal matrix by its transpose gives the Identity Matrix, $A^{T}A = I$, so its transpose is also its inverse: $A^{-1} = A^{T}$. That makes the inverse very cheap to compute.

The determinant of an orthogonal matrix is always 1 or -1, and the transformation it describes preserves lengths and angles (it's a rotation, a reflection or a combination of both).

See Week 4 - Matrices make linear mappings.