# Common Matrix Factor

Algebra Level 4

$AB = BA'$

Let $$A = \begin{bmatrix} 3 & 0 \\ 0 & 2 \end{bmatrix}$$, $$A' = \begin{bmatrix} 18 & 12 \\ -20 & -13 \end{bmatrix}$$, and $$B = \begin{bmatrix} a & b \\ c & d \end{bmatrix}$$, where $$a, b, c, d$$ are positive integers, satisfying the equation above.

If $$\det(B) = 1$$, compute $$a+b+c+d$$.

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