### Video Transcript

Given that π΄ is a matrix of order two by three and π΅ transpose is a matrix of order one by three, find the order of the matrix π΄π΅, if possible.

First, we need to determine whether itβs actually possible to find the product of the two matrices π΄ and π΅. Two matrices can only be multiplied if the number of columns in the first matrix is equal to the number of rows in the second. π΄ is a matrix of order two by three. This means that it has two rows and three columns. π΅ transpose is a matrix of order one by three, meaning it has one row and three columns. What about the matrix π΅? Well, the transpose of a matrix is found by swapping its rows and columns around. Therefore, the matrix π΅ will have three rows and one column.

In order to be able to find the product π΄π΅, we need the number of columns of the first matrix π΄ to be equal to the number of rows of the second matrix π΅. Theyβre both equal to three. And therefore, it is possible to find the product π΄π΅.

Now, we need to find the order of this matrix. If we multiply matrix of order π by π by matrix of order π by π, then the resulting matrix will have the same number of rows as the first matrix π and the same number of columns as the second matrix π. It will be of order π by π.

The number of rows in the first matrix π΄ is two. The number of columns in the second matrix π΅ is one. Therefore, the order of the matrix π΄π΅ is two by one.