OrthogonalMatrixQ

OrthogonalMatrixQ[m] gives True if m is an explicitly orthogonal matrix, and False otherwise.

Examples

Test for orthogonal matrix:

OrthogonalMatrixQ[{{1, 0}, {0, 1}}]
(* True *)

Rotation matrix:

OrthogonalMatrixQ[{{Cos[t], -Sin[t]}, {Sin[t], Cos[t]}}]
(* True *)

Please visit the official Wolfram Language Reference for more details.