Question

Write the addition and multiplication tables for (a) ${\mathit{z}}_{\mathbf{2}}\mathbf{\times }{\mathit{z}}_{\mathbf{3}}$(b)${\mathit{z}}_{\mathbf{2}}\mathbf{\times }{\mathit{z}}_{\mathbf{2}}$(c)${\mathit{z}}_{\mathbf{3}}\mathbf{\times }{\mathit{z}}_{\mathbf{3}}$

Short answer

Thus, the required answers are obtained.

Step-by-step solution

Write addition and multiplication table for z2×z3 

Write the addition table for $z_2\times z_3$as:

+	(0,0)	(0,1)	(1,0)	(1,1)	(2,0)	(2,1)
(0,0)	(0,0)	(0,1)	(1,0)	(1,1)	(0,0)	(0,1)
(0,1)	(0,1)	(0,2)	(1,1)	(1,2)	(0,1)	(0,2)
(1,0)	(1,0)	(1,1)	(0,0)	(0,1)	(1,0)	(1,1)
(1,1)	(1,1)	(1,2)	(0,1)	(0,2)	(1,1)	(1,2)
(2,0)	(0,0)	(0,1)	(1,0)	(1,1)	(0,0)	(0,1)
(2,1)	(0,1)	(0,2)	(1,1)	(1,2)	(0,1)	(0,2)

Write the multiplication table for $z_2\times z_3$ as:

$\times$	(0,0)	(0,1)	(1,0)	(1,1)	(2,0)	(2,1)
(0,0)	(0,0)	(0,0)	(0,0)	(0,0)	(0,0)	(0,0)
(0,1)	(0,0)	(0,1)	(0,0)	(0,1)	(0,0)	(0,1)
(1,0)	(0,0)	(0,0)	(1,0)	(1,0)	(0,0)	(0,0)
(1,1)	(0,0)	(0,1)	(1,0)	(1,1)	(0,0)	(0,1)
(2,0)	(0,0)	(0,0)	(0,0)	(0,0)	(0,0)	(0,0)
(2,1)	(0,0)	(0.1)	(0,0)	(0,1)	(0,0)	(0,1)

Write addition and multiplication table for z2×z2

Write the addition table for $z_2\times z_2$as:

+	(0,0)	(0,1)	(1,0)	(1,1)
(0,0)	(0,0)	(0,1)	(1,0)	(1,1)
(0,1)	(0,1)	(0,0)	(1,1)	(1,0)
(1,0)	(1,0)	(1,1)	(0,0)	(0,1)
(1,1)	(1,1)	(1,0)	(0,1)	(0,0)

Write the multiplication table for $z_2\times z_2$ as:

$\times$	(0,0)	(0,1)	(1,0)	(1,1)
(0,0)	(0,0)	(0,0)	(0,0)	(0,0)
(0,1)	(0,0)	(0,1)	(0,0)	(0,1)
(1,0)	(0,0)	(0,0)	(1,0)	(1,0)
(1,1)	(0,0)	(0,1)	(1,0)	(1,1)

Write addition and multiplication table for z3×z3

Write the addition table for $z_3\times z_3$as:

+	(0,0)	(0,1)	(0,2)	(1,0)	(1,1)	(1,2)	(2,0)	(2,1)	(2,2)
(0,0)	(0,0)	(0,1)	(0,2)	(1,0)	(1,1)	(1,2)	(2,0)	(2,1)	(2,2)
(0,1)	(0,1)	(0,2)	(0,0)	(1,1)	(1,2)	(1,0)	(2,1)	(2,2)	(2,0)
(0,2)	(0,2)	(0,0)	(0,1)	(1,2)	(1,0)	(1,1)	(2,2)	(2,0)	(2,1)
(1,0)	(1,0)	(1,1)	(1,2)	(2,0)	(2,1)	(2,2)	(0,0)	(0,1)	(0,2)
(1,1)	(1,1)	(1,2)	(1,0)	(2,1)	(2,2)	(2,0)	(0,1)	(0,2)	(0,0)
(1,2)	(1,2)	(1,0)	(1,1)	(2,2)	(2,0)	(2,1)	(0,2)	(0,0)	(0,1)
(2,0)	(2,0)	(2,1)	(2,2)	(0,0)	(0,1)	(0,2)	(1,0)	(1,1)	(1,2)
(2,1)	(2,1)	(2,2)	(2,0)	(0,1)	(0,2)	(0,0)	(1,1)	(1,2)	(1,0)
(2,2)	(2,2)	(2,0)	(2,1)	(0,2)	(0,0)	(0,1)	(1,2)	(1,0)	(1,1)

Write the multiplication table for $z_3\times z_3$as:

$\times$	(0,0)	(0,1)	(0,2)	(1,0)	(1,1)	(1,2)	(2,0)	(2,1)	(2,2)
(0,0)	(0,0)	(0,0)	(0,0)	(0,0)	(0,0)	(0,0)	(0,0)	(0,0)	(0,0)
(0,1)	(0,0)	(0,1)	(0,2)	(0,0)	(0,1)	(0,2)	(0,0)	(0,1)	(0,2)
(0,2)	(0,0)	(0,2)	(0,1)	(0,0)	(0,1)	(0,1)	(0,0)	(0,2)	(0,1)
(1,0)	(0,0)	(0,0)	(0,0)	(1,0)	(1,0)	(1,0)	(2,0)	(2,0)	(2,0)
(1,1)	(0,0)	(0,1)	(0,2)	(1,0)	(1,1)	(1,2)	(2,0)	(2,1)	(2,2)
(1,2)	(0,0)	(0,2)	(0,1)	(1,0)	(1,2)	(1,1)	(2,0)	(2,2)	(2,1)
(2,0)	(0,0)	(0,0)	(0,0)	(2,0)	(2,0)	(2,0)	(1,0)	(1,0)	(1,0)
(2,1)	(0,0)	(0,1)	(0,2)	(2,0)	(2,1)	(2,2)	(1,0)	(1,1)	(1,2)
(2,2)	(0,0)	(0,2)	(0,1)	(2,0)	(2,2)	(2,1)	(1,0)	(1,2)	(1,1)