MathDB

Peter wants to create a new multiplication table for the four numbers

1, 2, 3, 4

in such a way that the product of two of them is also one of them. He wants also that

(a\cdot b)\cdot c = a\cdot (b\cdot c)

holds and that

ab \ne ac

and

ba \ne ca

and

b \ne c

. Peter is successful in constructing the new table. In his new table,

1\cdot 3 = 2

and

2\cdot 2 = 4

. What is the product

3\cdot 1

according to Peter's table?

5