My friend and I figured it out together:
for (int i = 0; i < A.GetLength(0); i++)
for (int j = 0; j < A.GetLength(1); j++)
richTextBox1.AppendText(A[i,j] + " ");
richTextBox1.AppendText("\n"); //Just skips a line.
Woohooo! Programming is so satisfying once it makes a certain amount of sense. Total logic comes and goes.
Thanks for your help though, crew! It actually did end up helping a lot because it gave me a jump-off point.
So one of my instructors has given us a new assignment: prompt the user for two coordinates on a chessboard and calculate all possible moves that a knight can make. My first thought? "Checkmate! Only chess pieces allowed in Chessboard Land!"