Question Video: Finding the Product of Two Matrices

Video Transcript

Given that 𝐴 equals to negative seven, seven and 𝐵 equals to zero, negative five, find 𝐴𝐵 if possible.

You can multiply two matrices if and only if the number of columns in the first matrix equals the number of rows in the second. Otherwise, the product of two matrices is undefined. Here matrix 𝐴 has one column and matrix 𝐵 has one row. So we can multiply these matrices.

To find 𝐴𝐵 then, which is the product of matrix 𝐴 and matrix 𝐵, we need to do the dot product. Let’s do this for the first row in 𝐴 and the first column in 𝐵. Negative seven multiply by zero is zero. The first element in a matrix 𝐴𝐵 is therefore zero.

Then we multiply the elements in our first row of 𝐴 by the second element in 𝐵. Negative seven multiplied by negative five is 35. The element in the first row and second column of the product of 𝐴𝐵 is therefore 35. Multiplying seven by zero gives us zero.

The element in the first column and the second row of our product is therefore zero. Finally, we multiply seven by negative five to give us negative 35. And the final element of a product 𝐴𝐵 is negative 35. In this case then, 𝐴𝐵 is entirely possible and its matrix is as shown.