C++ - Determinant computation using recursion

The enclosed cpp file aims at calculating a matrix determinant using the following recursive formula:

$$ |A| = \sum_{j = 0}^{N-1}(-1)^{j}a_{0j}|\hat{A}_{0,j}|, $$

where, $A=(a_{ij})_{0\leq i,j\leq N-1}$ is a square matrix of order $N$, and

$\hat{A}_{0,j}$ is a modification of the matrix $A$ consisting in omitting its first row and $j$-th column, for all $0 \leq j \leq N-1$.