Matrix equations are mathematical expressions that involve matrices, which are rectangular arrays of numbers or symbols. These equations often take the form AX = B, where A is a matrix, X is the variable matrix we want to solve for, and B is another matrix. Matrix equations are commonly used in various fields, including engineering, computer science, and economics, to model and solve systems of linear equations. To solve a matrix equation, one typically uses methods such as matrix inversion or Gaussian elimination. If A is invertible, the solution can be found by multiplying both sides of the equation by the inverse of A, resulting in X = A⁻¹B. Understanding matrix equations is essential for working with linear systems and performing operations in higher-dimensional spaces.