Can you make MATLAB solve it?

In Linear Algebra, there are three cases for the solution of linear equation systems. That is, A linear equation system has no solution, exactly one solution or infinitely many solutions. Consider a linear equation system as A x = B where A is the coefficient matrix, x is the matrix of the unknown variables and B is the right hand side constants of the linear equation system. Let A|B be the augmented matrix. When rank of A is less than rank of AB, then it has no solution. Otherwise, when they are equal to each other, If the number of unknown variables is greater than rank of A or AB, then it has infinitely many solutions. If the number of unknown variables equals rank of A or AB, then it has exactly one solution. Write a MATLAB function named LinSysSolType that takes input arguments A and B and evaluates type of solution of linear equation system