Answer:
Let
(a, b) * (c, d) = (a + c, b + d)
=
(c + a, d + b)
=
(c, d) * (a, b)
is
commutative.
Also
((a, b) * (c, d) * (e, f)
=
(a + c, b + d) * (e, f)
=
((a + c) + e, (b + d) + f)
=
(a + (c + e), b + (d + f))
=
(a, b) * (c + e, d + f)
=
(a, b) * ((c, d) * (e, f))
is
associative.
To
find the identity element.
Let
(x, y) be the identity element.
Let
(x, y) be the identity element.
a + x = a
and b + y = 6
x = 0 and y
= 0
is the
identity element.
But
(0, 0)
so Identity
element does not exist.
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