MathDB

1979 VTRMC #3

Source:

August 8, 2018

Problem Statement

Let

A

be an

n\times n

nonsingular matrix with complex elements, and let

\overline{A}

be its complex conjugate. Let

B = A\overline{A}+I

, where

I

is the

n\times n

identity matrix. (a) Prove or disprove:

A^{-1}BA = \overline{B}

. (b) Prove or disprove: the determinant of

A\overline{A}+I

is real.

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