A magic square is an array of numbers in which the sum of the numbers in each row, in each column, and along the two main diagonals is equal. Consider the following 3x3 magic square where the numbers are in base \( b \):

\[
\begin{matrix}
1 & 10 & 11 \\
13 & 3 & 4 \\
12 & 2 & 14 \\
\end{matrix}
\]

Determine the base \( b \) such that the square is a magic square. Let's think step by step and output the final answer within \boxed{}.
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