16.-Linear-Algebra-by-Kenneth-Hoffman · Problem 5.4.5

Determinants

Mathematics — Linear Algebra · unitary-matrix-determinant

Problem

n \times n

matrix

A

over the field of complex numbers is said to be unitary if

AA^* = I

(

A^*

denotes the conjugate transpose of

A

). If

A

is unitary, show that

|\det A| = 1