Matrix Multiplication

Algebra Level 3

Let \(A, B\) and \(C\) be matrices such that \( A = \begin{pmatrix} 1 & 2 \\ 3 & 1 \\ 2 & 3 \end{pmatrix} \), \( B = \begin{pmatrix} 1 & 2 & 2 \\ 2 & 4 & 3 \end{pmatrix} \) and \(C=AB\).

What is the sum of all the elements (entries) of matrix \(C\)?

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