exists an element b in A such that a ∗ b = e = b ∗ a and b is called the inverse of a and is denoted by a – 1 .
Numerical : Show that – a is the inverse of a for the addition operation ‘+’ on R and 1 / a is the inverse of a ≠ 0 for the multiplication operation ‘×’ on R .
Solution : -a + a = 0 = a + ( -a ), so – a is inverse of a , where a ∈ R 1 / a * a = 1 = a * 1 / a where a ∈ { R-0 }, for a = 0 , this will not hold true Thus -a is additive inverse of a & 1 / a is multiplicative inverse of a .