### Video Transcript

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

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 πΆ is equal to matrix π΄π΅ plus matrix π΄πΆ. It is important to note though that
if the parentheses came first, we were multiplying π΅ plus πΆ by π΄, then our answer
would be π΅π΄ plus πΆπ΄. 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 πΆ is
equal to π΄π΅ plus π΄πΆ.

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 πΆ,
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 πΆ.