Prove, that H(XY) = H(X) + H(Y) (entropy theory)

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If two independent sources have entropy

$$H\left(XY\right)=\sum _{j=1}^N\cdot \sum _{i=1}^Mp_iq_j\log\left(p_iq_j\right)$$

Prove

$H(XY) = H(X) + H(Y)$