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
jamb 2021mathematics

The correct answer is D. e = 0

The identity element e for the binary operation \(\ast\) defined by m \(\ast\) n = mn + m + n for any real number m and n is the element such that m \(\ast\) e = m for any real number m.

Substituting the definition of the binary operation \(\ast\) into the equation m \(\ast\) e = m, we get:

m \(\ast\) e = me + m + e = m

Solving this equation for e, we get:

me + m + e = m

me + e = 0

e(m + 1) = 0

Since this equation must hold for any real number m, we must have e = 0.

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