Question

Write out the addition and multiplication tables for \[{{\rm{Z}}_6}\] (where by addition and multiplication we mean \[{ + _6}{\rm{ and }}{ \cdot _6}\]).

Short answer

The addition table for \[{Z_6}\]is:

\[{ + _6}\]	\[0\]	\[1\]	\[2\]	\[3\]	\[4\]	\[5\]
\[0\]	\[0\]	\[1\]	\[2\]	\[3\]	\[4\]	\[5\]
\[1\]	\[1\]	\[2\]	\[3\]	\[4\]	\[5\]	\[0\]
\[2\]	\[2\]	\[3\]	\[4\]	\[5\]	\[0\]	\[1\]
\[3\]	\[3\]	\[4\]	\[5\]	\[0\]	\[1\]	\[2\]
\[4\]	\[4\]	\[5\]	\[0\]	\[1\]	\[2\]	\[3\]
\[5\]	\[5\]	\[0\]	\[1\]	\[2\]	\[3\]	\[4\]

Step-by-step solution

Step 1

The multiplication table for \[{Z_6}\]is:

\[{ \cdot _6}\]	\[0\]	\[1\]	\[2\]	\[3\]	\[4\]	\[5\]
\[0\]	\[0\]	\[0\]	\[0\]	\[0\]	\[0\]	\[0\]
\[1\]	\[0\]	\[1\]	\[2\]	\[3\]	\[4\]	\[5\]
\[2\]	\[0\]	\[2\]	\[4\]	\[0\]	\[2\]	\[4\]
\[3\]	\[0\]	\[3\]	\[0\]	\[3\]	\[0\]	\[3\]
\[4\]	\[0\]	\[4\]	\[2\]	\[0\]	\[4\]	\[2\]
\[5\]	\[0\]	\[5\]	\[4\]	\[3\]	\[2\]	\[1\]