Start by creating a C$++$ template matrix class with only basic linear algebra functionality

a$)$

Extend this class to also perform matrix inversions.

b$)$

Further extend the class to perform stream input and output operations.

c$)$

Create a driver program that uses this overall class from $($a$)$ and $($b$)$ to read a matrix from a user specified filename, invert the matrix, and save the inverted matrix in a file with a new name. Then multiply the original and inverted matrices to show that they are equal to the identity matrix.