An inverse element in mathematics refers to an element that, when combined with another element using a specific operation, results in the identity element of that operation. For example, in addition, the inverse of a number a is -a because a + (-a) = 0 , where 0 is the identity element for addition. Similarly, in multiplication, the inverse of a number b is \frac1b since b \times \frac1b = 1 , with 1 being the identity element for multiplication. Inverse elements are crucial in various mathematical structures, such as groups, rings, and fields. In these structures, every element must have an inverse to satisfy certain properties. For instance, in the set of integers under addition, every integer has an inverse (its negative), while in the set of non-zero rational numbers under multiplication, every number has an inverse (its reciprocal