Matrix Manipulation library in C

Let's say you want to develop a Matrix manipulation library in pure C (not C++). For example, you want to define a "matrix_multiply" function to get A * B, how to declare the function and how to implement it? Make sure that you consider error handling stuff, e.g., a 2*2 matrix and a 3*3 matrix cannot multiply, and how to detect and deal with the situation when you pass a 3*3 matrix as a parameter which should actually be 2*2.