The IsOrthogonal(A) command determines if  is an orthogonal Matrix (, where  is the transpose and  is the identity Matrix).

In general, the IsOrthogonal command returns true if it can determine that Matrix  is orthogonal, false if it can determine that the Matrix is not orthogonal, and FAIL otherwise.

The IsUnitary(A) command determines if  is a unitary Matrix (, where  is the Hermitian transpose and  is the identity Matrix).

In general, the IsUnitary command returns true if it can determine that Matrix  is unitary, false if it can determine that the Matrix is not unitary, and FAIL otherwise.