JAMB 2012 Mathematics · Question 39

The binary operation on the set of real numbers is defined by m*n = $\frac{mn}{2}$ for all m, n $\in$ R. If the identity element is 2, find the inverse of -5

Options

A. $-\frac{4}{5}$
B. $-\frac{2}{5}$
C.4
D.5

Answer: A. $-\frac{4}{5}$

Explanation written with AI and checked against the answer key

Analyze the question: The operation is mn = mn/2. We are told the identity element is 2, and we need the inverse of -5. Concept: The identity element e satisfies me = m. The inverse of m, written m⁻¹, satisfies mm⁻¹ = e. Check the identity: me = me/2 = m, so e = 2. This matches the given identity. Find the inverse of -5: Let the inverse be x. Then (-5)x = e = 2 (-5)(x)/2 = 2 -5x = 4 x = -4/5 Check: (-5)(-4/5) = (4)/2 = 2 ✓ Tip: For any inverse question, set m*x = e and solve for x. In this operation, the general inverse is m⁻¹ = 4/m, so for -5 you get 4/(-5) = -4/5. Always verify by plugging back in to confirm you get the identity.

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The binary operation on the set of real numbers is defined by m*n = mn2\frac{mn}{2}2mn​ for all m, n ∈\in∈ R. If the identity element is 2, find the inverse of -5

Options

Answer: A. −45-\frac{4}{5}−54​

The binary operation on the set of real numbers is defined by m*n = $\frac{mn}{2}$ for all m, n $\in$ R. If the identity element is 2, find the inverse of -5

Answer: A. $-\frac{4}{5}$