Design a class to perform various matrix operations. A matrix is a set of numbers arranged in rows and columns. Therefore, every element of a matrix has a row position and a column position. If A is a matrix of 5 rows and 6 columns, we say that matrix A is of the size 5 x 6 and sometimes denote it as A5x6. Clearly, a convenient place to store a matrix is in a two-dimensional array. Two matrices can be added and subtracted if they have the same size. Suppose that A = [a_ij] and

B = [bij] are two matrices of the size m x n, where aij denotes the element of A in the ith row and the jth column, and so on. The sum and difference of A and B is given by

The multiplication of A and B (A * B) is defined only if the numberof columns of A are the same as the number of rows of B. If A is of thesize m xn and B is of the size n xt, then A * B =[cik] is of the size m xtand the element cik is given by the formula

 

Design and implement a class matrixType that can store a matrix of any size. Overload the operators +, -, and * to perform the addition, subtraction, and multiplication operations, respectively, and overload the operator <<to output a matrix. Also, write a test program to test various operations on matrices.