Calculating the determinant of a matrix - c++

Question

I am trying to calculate the determinant of a square matrix using row operations.
I ran into this code but I do not really understand how it works.
What do subi and subj do? Does it use row operations?
What is the logic behind this code?
int c, subi, i, j, subj;
double submat[10][10],d=0;
if (n == 2) {
return((mat[0][0] * mat[1][1]) - (mat[1][0] * mat[0][1]));
}
else {
for (c = 0; c < n; c++) {
subi = 0;
for (int i = 1; i < n; i++) {
subj = 0;
for (j = 0; j < n; j++) {
if (j == c)
continue;
submat[subi][subj] = mat[i][j];
subj++;
}
subi++;
}
d = d + (pow(-1, c)*mat[0][c] * determinant(n - 1, submat));
}
}
return d;

Answer 1

The function, which looks like:
double determinant(int n, double mat[10][10]);
recursively goes through rows and calls itself on the submatrices for that row and the first column return a value for all by matrices. The recursion ends for 2 by 2 matrices.

Answer 2

This is a recursive function using Laplace expansion to calculate the determinant whose base case is a 2 by 2 matrix.
However, it does not seem to be a good program to me for:
what if the input is a 1 by 1 matrix
submat is limited by size of 10 by 10
submat is a waste of memory
When matrix is large, it is better to use LU decomposition.