(a) Verify the entries given in Table 5.2 for the multiplication table of \(\mathrm{C}_{3 \mathrm{v}}\).

(b) Show that the multiplication table for \(\mathrm{C}_{3 \mathrm{v}}\) can be put into one to one correspondence with that in Table 2.2 for \(\mathrm{S}_{3}\).

Data from Table 5.2

Data from Table 2.2

Table 5.2. Multiplication table A - B for C3v A\B | e C3 C3 e C3 e 3 e C3 e e 0 a e C3 e 3