Thread: Creating and freeing dynamic arrays

I am trying to write my own class Matrix that dynamically allocates two dimensional arrays and contains functions to perform addition, subtraction etc on objects of class Matrix. I have a few questions related to dynamic arrays:
1. Must an array dynamically allocated using new be freed by delete? If a temporary object of class Matrix is declared within a function, will the memory be freed every time the function returns?
2. I have written my program (could provide code if needed) without any destructors at all. Would I face any trouble later since allocated memory has not been freed? I have also overloaded the "=" operator so that a statement involving objects like:

Code:

a=b;

Will result in the dynamic array in object "a" to be allocated using new with respect to the rows and columns of "b". The function is:

Code:

// Assigning one matrix to another.
	Matrix operator=(const Matrix &mat2) {
		int x, y;
		dimension_check(mat2);
/*		for (x=0;x<rows;x++) {
			delete [] mat_var[x];
		}
		delete [] mat_var; */
		rows=mat2.rows;
		columns=mat2.columns;
		create_matrix();
		for (x=0;x<mat2.rows;x++) {
			for (y=0;y<mat2.columns;y++) {
				mat_var[x][y]=mat2.mat_var[x][y];
			}
		}
		return *this;
	}

Please note that part where delete [] has been commented out. The program woks only with these commented. However, the program also works when a Matrix that has been initially allocated as 2*2 is equated to a matrix of 3*1. I have the feeling I am doing something fundamentally wrong by reallocating without any delete [] statement after reading some of the previous posts in this forum. People recommend allocating new memory, copying and then deleting new memory. However, if by equating a=b, it is implied that the contents of "a" are not needed, then could a copy be skipped? But to allocate new dimensions of memory would a delete not be required?
The function create_matrix() is:

Code:

	void create_matrix() {
		try {
			mat_var=new float *[rows];
		}
		catch (std::bad_alloc xa) {
			std::cout << "Out of memory.\n";
			exit(1);
		}
		int row_count;
		for (row_count=0;row_count<rows;row_count++) {
			try {
				mat_var[row_count]=new float [columns];
			}
			catch (std::bad_alloc xa) {
				std::cout << "Out of memory.\n";
				exit(1);
			}
		}
		return;
	}

Thanks.