Linear Algebra is the study of systems of linear equations, with applications in vector spaces and linear mapping. Such equations are usually represented in the form of matrices, where terms such as determinant and inverse are extremely important for the study of these matrices. One central problem that is commonly tackled in linear algebra is finding the solution of a matrix equation. For example, a particular matrix can be written in the following way:

Ax = B

Where,

A is the matrix describing the system of linear equation

B is the set of constants

x is the set of unknown variables

This particular equation can be solved using the inverse of the matrix, which is commonly denoted as A^(-1)

So by multiplying both sides of the equation by the inverse of A, then the following results:

A^(-1)*Ax = A^(-1)*B

X = A^(-1)*B

In this light, it can be seen that only the inverse of the matrix needs to be calculated to solve the linear equation. Thus, understanding the applicability of the rules and properties of matrices is important for being able to solve linear equations.