Design a class to perform various matrix operations. A matrix is a set of numbers arrang...

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 five rows and six columns, we say that the matrix A is of the size 5 × 6 and sometimes denote it as A5_5×6. 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 A = [aij] and B = [bij] are two matrices of the size m _ n, in which 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 are given by:

The multiplication of A and B (A * B) is defined only if the number of columns of A is the same as the number of rows of B. If A is of the size m × n and B is of the size n × t, then A *B = [c_ik] is of the size m × t and the element cik is given by the formula:

Design and implement a class matrixType that can store amatrix 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 the matrices.