What is the process for creating a `%*%` function for a basic matrix S3 subcategory?

edit

Here is a the process for creating a %*% function for a basic matrix S3 subcategory:

1. Define the class of the matrix object. For example, let's say we want to create a %*% function for a matrix class called basicmatrix.

2. Create a constructor function that creates instances of the basicmatrix class. This function should take one argument, which is a vector or list that contains the data for the matrix. This function should also set the class attribute of the object to basicmatrix.

3. Define a %*% function for the basicmatrix class. This function should take two arguments, which are instances of the basicmatrix class. The function should check that the dimensions of the matrices are compatible for matrix multiplication (i.e. the number of columns in the first matrix must equal the number of rows in the second matrix). If the dimensions are compatible, the function should perform matrix multiplication using the standard procedure. The output should be an instance of the basicmatrix class.

4. Define any other methods that are necessary for the basicmatrix class. For example, you might want to define a print method that prints out the matrix in a nice format.

5. Test the %*% function and other methods with some basic examples to ensure that they work correctly.