# Question Video: Distributing Matrix Multiplication over Addition Mathematics

Given three matrices π΄, π΅, and πΆ, which of the following is equal to π΄(π΅ + πΆ)? [A] π΄π΅ + πΆ [B] π΄π΅ + π΄πΆ [C] π΅π΄ + πΆπ΄ [D] π΅π΄ + πΆ [E] π΅ + π΄πΆ

01:56

### Video Transcript

Given three matrices π΄, π΅, and πΆ, which of the following is equal to π΄ multiplied by π΅ plus πΆ? Is it (A) π΄π΅ plus πΆ, (B) π΄π΅ plus π΄πΆ, (C) π΅π΄ plus πΆπ΄, (D) π΅π΄ plus πΆ, or (E) π΅ plus π΄πΆ?

In order to answer this question, we need to use the distributive property of matrices. We can distribute matrices in a similar way to how we distribute real numbers. Multiplying matrix π΄ by matrix π΅ plus πΆ is equal to matrix π΄π΅ plus matrix π΄πΆ. It is important to note though that if the parentheses came first, we were multiplying π΅ plus πΆ by π΄, then our answer would be π΅π΄ plus πΆπ΄. If the matrix π΄ is distributed from the left side, we must ensure that the product in the resulting sum has π΄ on the left. In the same way, if matrix π΄ is distributed from the right side, each product in the resulting sum must have π΄ on the right. We can therefore see that the correct answer is option (B). π΄ multiplied by π΅ plus πΆ is equal to π΄π΅ plus π΄πΆ.

It is important to remember that when performing matrix addition and matrix multiplication, the order of each matrix is key. In order to add matrix π΅ and πΆ, they must have the same order. To perform matrix multiplication, the number of columns in matrix π΄ must be equal to the number of rows in matrix π΅ and πΆ.