The document discusses finding the inverse of square matrices to solve systems of linear equations. It defines an inverse matrix as a matrix that when multiplied by the original matrix results in the identity matrix. For a matrix to have an inverse, it must be nonsingular. The document presents methods for finding the inverse of 2x2 and 3x3 matrices, including using the determinant and shortcut formulas. It explains how to use the inverse of the coefficient matrix to solve systems of linear equations. Examples are provided to illustrate calculating inverses and using them to solve systems.