Let A and B be rings. Define addition and multiplication on the Cartesian product A x B by (x,y) + (x', y') = (x + x', y + y') and (x, y)(x', y') = (xx', yy'). Show that the A x B is also a ring. When is A x B commutative? When is it a ring with unity? Deduce from these facts that Z₂ x Z3 is a commutative ring with unity write down its addition and multiplication tables.

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