Give the matrix equation below, what is the value of \(ab\) ?

$$ \begin{bmatrix} 5 & -6 \\ 3 & 12 \end{bmatrix} + \begin{bmatrix} a & 2 \\ 0 & b \end{bmatrix} = \begin{bmatrix} 10 & -4 \\ 3 & 4 \end{bmatrix} $$

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Matrix addition invovles addition of corresponding entries.

$$ \begin{bmatrix} 5 & -6 \\ 3 & 12 \end{bmatrix} + \begin{bmatrix} a & 2 \\ 0 & b \end{bmatrix} = \begin{bmatrix} 10 & -4 \\ 3 & 4 \end{bmatrix} $$ $$ ab = (-5)(-8) = \boxed{-40} $$