Matrix reloaded ... or reversed

I have written this Matrix class after posting an answer to Malachi's rags-to-riches question. The initial purpose had been to reverse a matrix represented by a 2D array. I have changed it to a more object-orientated version.

Just for fun, I have added the ability to sum two Matrix objects:

public class Matrix
{
    private int[][] internalMatrix;
    private int rowCount = -1;
    private int columnCount = -1;

    private Matrix(int rowCount, int columnCount)
    {
        this.rowCount = rowCount;
        this.columnCount = columnCount;
        Initialize();
    }
    private void Initialize()
    {
        internalMatrix = new int[rowCount][];
        for (int rowIndex = 0; rowIndex = 0; i--)
        {
            matrix.internalMatrix[i] = GetReversedRowValues(rowIndex);
            rowIndex++;
        }
        return matrix;
    }
    private int[] GetReversedRowValues(int rowIndex)
    {
        int[] reversedRow = new int[columnCount];
        int j = 0;
        for (int i = columnCount - 1; i >= 0; i--)
        {
            reversedRow[j] = this[rowIndex, i];
            j++;
        }
        return reversedRow;
    }
    public static Matrix operator +(Matrix first, Matrix second)
    {
        if (first.rowCount != second.rowCount || first.columnCount != second.columnCount)
        {
            throw new NotSupportedException("For adding 2 matrix they need to have the same row and columcount");
        }

        Matrix sum = new Matrix(first.rowCount, first.columnCount);
        for (int rowIndex = 0; rowIndex < first.rowCount; rowIndex++)
        {
            for (int columnIndex = 0; columnIndex < first.columnCount; columnIndex++)
            {
                sum[rowIndex, columnIndex] = first[rowIndex, columnIndex] + second[rowIndex, columnIndex];
            }
        }
        return sum;
    }
}

And can be called like:

```
Matrix matrix = new Matrix(new int[,]
{
{1, 2, 3},
{4, 5, 6},
{7, 8, 9}
}

to make this a little clearer you can declare more than one incrementation variable inside your for loop

private int[] GetReversedRowValues(int rowIndex)
{
    int[] reversedRow = new int[columnCount];
    int j = 0;
    for (int i = columnCount - 1; i >= 0; i--)
    {
        reversedRow[j] = this[rowIndex, i];
        j++;
    }
    return reversedRow;
}

like this

private int[] GetReversedRowValues(int rowIndex)
{
    int[] reversedRow = new int[columnCount];
    for (int i = columnCount - 1, j = 0; i >= 0; i--, j++)
    {
        reversedRow[j] = this[rowIndex, i];
    }
    return reversedRow;
}

I don't know what the standard on doing this is, but it seems like a good idea especially for reversing an array.

StackExchange Code Review Q#66847, answer score: 5