An operation is defined on the set of real numbers by ab = a + b + 1. If the identity elements is -1, find the inverse of the element 2 under .

  • A 4
  • B zero
  • C -2
  • D -4
jamb 2001mathematics

The correct answer is D. -4

The identity element for the operation is given as -1, which means that for any real number \(a\), we have \(a (-1) = -1 a = a\).

Now, let's find the inverse of the element 2 under the operation . We are looking for a number \(b\) such that \(2 b = -1\).

Using the definition of the operation , we have:

\(2 b = 2 + b + 1\)

Simplifying:

\(2 + b + 1 = -1\)

Combining like terms:

\(3 + b = -1\)

Now, subtracting 3 from both sides:

\(b = -4\)

So, the inverse of the element 2 under the operation is -4.

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