import java.util.stream.IntStream;

public class Determinant {

	public static double det(double[][] matrix) {
		final double EPS = 1e-10;
		int n = matrix.length;
		double[][] a = IntStream.range(0, n).mapToObj(i -> matrix[i].clone()).toArray(double[][]::new); // make a copy
		double res = 1;
		for (int i = 0; i < n; i++) {
			int p = i;
			for (int j = i + 1; j < n; j++)
				if (Math.abs(a[j][i]) > Math.abs(a[p][i]))
					p = j;
			if (Math.abs(a[p][i]) < EPS)
				return 0;
			if (i != p) {
				res = -res;
				double[] t = a[i];
				a[i] = a[p];
				a[p] = t;
			}
			res *= a[i][i];
			for (int j = i + 1; j < n; j++)
				a[i][j] /= a[i][i];
			for (int j = 0; j < n; ++j)
				if (j != i && Math.abs(a[j][i]) > EPS /*optimizes complexity to O(n^2) for sparse matrices*/)
					for (int k = i + 1; k < n; ++k)
						a[j][k] -= a[i][k] * a[j][i];
		}
		return res;
	}

	// Usage example
	public static void main(String[] args) {
		double d = det(new double[][]{{0, 1}, {-1, 0}});
		System.out.println(Math.abs(d - 1) < 1e-10);
	}
}

import java.util.stream.IntStream;

public class Determinant {

	public static double det(double[][] matrix) {
		final double EPS = 1e-10;
		int n = matrix.length;
		double[][] a = IntStream.range(0, n).mapToObj(i -> matrix[i].clone()).toArray(double[][]::new); // make a copy
		double res = 1;
		for (int i = 0; i < n; i++) {
			int p = i;
			for (int j = i + 1; j < n; j++)
				if (Math.abs(a[j][i]) > Math.abs(a[p][i]))
					p = j;
			if (Math.abs(a[p][i]) < EPS)
				return 0;
			if (i != p) {
				res = -res;
				double[] t = a[i];
				a[i] = a[p];
				a[p] = t;
			}
			res *= a[i][i];
			for (int j = i + 1; j < n; j++)
				a[i][j] /= a[i][i];
			for (int j = 0; j < n; ++j)
				if (j != i && Math.abs(a[j][i]) > EPS /*optimizes overall complexity to O(n^2) for sparse matrices*/)
					for (int k = i + 1; k < n; ++k)
						a[j][k] -= a[i][k] * a[j][i];
		}
		return res;
	}

	// Usage example
	public static void main(String[] args) {
		double d = det(new double[][]{{0, 1}, {-1, 0}});
		System.out.println(Math.abs(d - 1) < 1e-10);
	}
}

Update Determinant.java