Kunze Linear Algebra · Problem 5.3.1

Determinants

Mathematics — Methods · determinant-skew-symmetric

Problem

K

is a commutative ring with identity and

A

is the matrix over

K

given by

A = \begin{bmatrix} 0 & a & b \\ -a & 0 & c \\ -b & -c & 0 \end{bmatrix}

show that

\det A = 0