Kunze Linear Algebra · Problem 1.2.5

Systems of Linear Equations

Mathematics — Methods · finite-fields

Problem

Let

F

be a set which contains exactly two elements,

0

and

1

. Define an addition and multiplication by the tables:

\begin{array}{c|cc} + & 0 & 1 \\ \hline 0 & 0 & 1 \\ 1 & 1 & 0 \end{array} \qquad \begin{array}{c|cc} \cdot & 0 & 1 \\ \hline 0 & 0 & 0 \\ 1 & 0 & 1 \end{array}

Verify that the set

F

, together with these two operations, is a field.