The inverse of a is 1 / a, so that a × 1 / a = 1. We must stress that a ≠ 0. The inverse is the reciprocal.

 

The inverse creates the identity. For multiplication (or division), the identity is 1. For addition (or subtraction) the identity is 0, and so the inverse changes the sign. The inverse of a is –a.

 

Students may confuse the words “inverse” and “identity”. This should be clarified with examples.