If I write $$\sum_{i=1}^{10}\sum_{j=1}^{10} |a_{ij}| \ ||B||_2$$ then is it the same as $$\sum_{i=1}^{10}\left(\sum_{j=1}^{10} \left(|a_{ij}|\right) \right)\ ||B||_2$$ or $$\sum_{i=1}^{10}\left(\sum_{j=1}^{10} \left(|a_{ij}| \ ||B||_2\right)\right)$$
In other words, does $\sum$ only take the left most term, all terms, or is it ambiguous?
Both of your terms with the parentheses are correct, since $\|B\|_2$ is independent of the summations anyhow. All three of the terms you gave are the same as $$ \|B\|_2 \sum_{i=1}^{10}\sum_{j=1}^{10} |a_{ij}|$$