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

The identity element of a binary operation is an element "e" in a set such that for any element "x" in the same set, the result of the binary operation "e * x" or "x * e" is equal to "x". In other words, it's an element that doesn't change the result when it's multiplied with any other element. In this case, if we set "m = e" and "n = 0", the equation becomes: "e * 0 + e + 0 = e". This means that the identity element for this binary operation is "e = 0". So, the answer is: "e = 0".