Inverse operations

In mathematics, an inverse operation is an operation reversing the effect of another operation. Addition and subtraction, as well as multiplication and division are inverse operations.

This is quite noticeable when investigating matrices. Because division is impossible when analysing matrices, a matrix called the 'inverse matrix' is used. The inverse matrix has the property such that the matrix, multiplied by the inverse matrix equals the identity matrix ([I], the matrix which contains 1s on the topleft-bottomright diagonal, and zeros everywhere else), the matrix-equivalent of 1. For example, consider the matrix equation: [A][B]=[C] to put this into the form [A]= , one must use the inverse matrix of [B] (usuallly represented by B with the superscript -1). [A][B][B^-1]=[C][B^-1] Because [B][B^-1]=[I], [A]=[C][B^-1]. This operation is only possible because of inverse operations.