The document provides examples for solving matrix equations using inverses. It introduces the concept of pre-multiplying both sides of a matrix equation AX=B by the inverse of A to solve for X. Example 1 demonstrates this process, finding the inverse of the coefficient matrix and multiplying both sides to isolate X. Example 2 shows that the inverse does not exist when the coefficient matrix is singular, meaning there may be no solution or infinite solutions depending on whether the rows of B satisfy the relationship of the rows of the singular A.