Find '?' in a $3 \times 3$ array of integers

Question

I had trouble cracking this little puzzle from an elementary school 'math olympiad'. Find the missing number '?' in this array:

$\begin{bmatrix} 4 & 1 & 2\\2 & 6 & 4\\3 & 2 & ?\end{bmatrix}$

Of course the real problem doesn't involve matrices. It's just a 3 by 3 grid with numbers. Somehow I an unable to find any pattern in this array.

Answer 1

If you look at the $2\times2$ block you see that those $3$ which we are able to calculate all sum up to $13$. If you put $1$ in the "?". Then that $2\times2$ block also sums up to $13$.

Answer 2

I got 3, so all columns sum up to 9

Answer 3

I got 3 as well, since it's the decimal next to the first occurence of 41226432 in $\pi$'s decimals.

Answer 4

One can create a polynomial in two variables A(x,y) such that A(i,j) = the known i,j th entries of the matrix and A(3,3) = any number you like. So the answer is any number you like. That should make it easy for elementary school kids.
I like 24/11, which makes the determinant 0.