Given this matrix:

\begin{matrix}
2 & 3 & 0 & 9 & 0 & 1 & 0 & 1 & 1 & 2 & 1 \\
1 & 1 & 0 & 3 & 0 & 0 & 0 & 9 & 2 & 3 & 1 \\
1 & 4 & 0 & 2 & 8 & 5 & 0 & 3 & 6 & 1 & 9 \\
0 & 0 & 0 & 0 & 0 & 5 & 0 & 0 & 0 & 0 & 0 \\
2 & 2 & 4 & 1 & 1 & 2 & 1 & 6 & 9 & 0 & 7 \\
0 & 0 & 0 & 6 & 0 & 7 & 0 & 1 & 0 & 0 & 0 \\
2 & 5 & 0 & 7 & 0 & 4 & 6 & 8 & 5 & 1 & 3 \\
0 & 0 & 0 & 1 & 0 & 4 & 0 & 1 & 0 & 0 & 0 \\
0 & 0 & 0 & 8 & 0 & 2 & 0 & 0 & 0 & 0 & 0 \\
2 & 1 & 0 & 0 & 0 & 1 & 0 & 0 & 2 & 1 & 1 \\
2 & 6 & 0 & 1 & 0 & 30 & 0 & 2 & 3 & 2 & 1 \\
 \end{matrix}

Is there an efficient way of calculating its determinant using the matrix minors? it just seems that there's lots of zeroes inside so it has to ease up the operation and I'm missing something.

Thanks.