If the binary operation ∗ ∗ is defined by m ∗ ∗ n = mn + m + n for any real number m and n, find the identity of the elements under this operation

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

Answer Details

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