If the binary operation (ast) is defined by m (ast) n = mn + m + n for any real number m and n, find the identity of the elements under this operation
-
A.
e = 1 -
B.
e = -1 -
C.
e = -2 -
D.
e = 0
Correct Answer: Option B
Explanation
m (ast) n = mn + m + n
m (ast) e = me + m + e, e (ast) m = e
∴ me + m + e, m(e + 1)e – e = 0
e + 1 = 0
∴ e = -1