Show that this matrix is invertible I have the following exercise:
Show that the matrix $A=(a_{ij})$ where $a_{ij}=i^{j-1}$, $i,j=1, \dots n$ is invertible.
Do I have to show that the determinant is equal to $0$?

From the wiki article on Vandermonde matrices, the determinant of the mentioned matrix would be
$$det = \prod_{1 \le i < j \le n}(j - i)$$
But since $j > i$, the above product will always be positive, i.e. not equal to $0$.
