Exercise 11.11.8

Avg difficulty 3.0

Assume $A$ and $B$ are hermitian $3\times 3$ -matrices, and $A$ is invertible. Then which of the following matrices are hermitian?

(a)~{}AB\quad(b)~{}A+B\quad(c)~{}iA\quad(d)~{}-A\quad(e)~{}2A\quad(f)~{}A^{*}BA\quad(g)~{}A^{-1}BA\quad(h)~{}BB^{*}\quad(i)~{}A^{2}

Selinger, Matrix Theory and Linear Algebra, Inner product spaces, Unitary and hermitian matrices, Exercise 11.11.8

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Adapted from Matrix Theory and Linear Algebra © 2017–2026 Peter Selinger, Lyryx Learning, and Ken Kuttler. Licensed under CC BY 4.0. Source: Matrix Theory and Linear Algebra. Imported at revision d74bc3a.