Determinant of a matrix

This little program calculates the determinant of an matrix.. using recursion. You don't even need ad - bc for a 2x2 [[a b][c d]] https://en.wikipedia.org/wiki/Determinant

public class CodeWar {

	public static int[][] buildSubmatrix(int[][] matrix, int r, int c) {
		int size = matrix.length - 1;
		int result[][] = new int[size][size];
		int a = 0, b = 0;

		for (int i = 0; i < matrix.length; i++) {
			for (int j = 0; j < matrix.length; j++) {
				if (i != 0 && j != c) {
					result[a][b] = matrix[i][j];
					b++;
				}
			}
			if (i != r) {
				a++;
				b = 0;
			}
		}
		return result;
	}


	public static int determinant(int[][] matrix) {
		if (matrix.length == 1)
			return matrix[0][0];

		int sign = 1;
		int sum = 0;
		for (int i = 0; i < matrix[0].length; i++) {
			int n = matrix[0][i];
			int submatrix[][] = buildSubmatrix(matrix, 0,i);
			sum += sign * n * determinant(submatrix);

			sign = sign * -1;
		}
		return sum;

	}

	public static void main(String arg[]) {
		int[][] matrix = { 
				{ -2, -1,2 }, 
				{ 2,1,4 }, 
				{ -3,3,1 } };
		System.out.println(determinant(matrix));
	}
}