Editing Matrix multiplication (section)

===Distributivity===
The matrix product is [[distributive property|distributive]] with respect to [[matrix addition]]. That is, if {{math|'''A''', '''B''', '''C''', '''D'''}} are matrices of respective sizes {{math|''m'' × ''n''}}, {{math|''n'' × ''p''}},  {{math|''n'' × ''p''}}, and {{math|''p'' × ''q''}}, one has (left distributivity)
:<math>\mathbf{A}(\mathbf{B} + \mathbf{C}) = \mathbf{AB} + \mathbf{AC},</math>
and (right distributivity)
:<math>(\mathbf{B} + \mathbf{C} )\mathbf{D} = \mathbf{BD} + \mathbf{CD}.</math><ref name=":2" />

This results from the distributivity for coefficients by 
:<math>\sum_k a_{ik}(b_{kj} + c_{kj}) = \sum_k a_{ik}b_{kj} + \sum_k a_{ik}c_{kj} </math>
:<math>\sum_k (b_{ik} + c_{ik}) d_{kj} = \sum_k b_{ik}d_{kj} + \sum_k c_{ik}d_{kj}. </math>