There are three Excel files available for download at www.mathsfiles.com/Excel_Files under A/AS Pure Files that can help with explaining these processes in a visual and interactive may.
Sometimes a picture is worth a thousand words and I find that once students see these operations explained in this graphic way they “get it” and remember it in a quick and natural way.
The files use Macros so that if you click on an element the highlighting will change dynamically to show the how the calculation is done.
The entries in the Matrices can also be changed to generate new examples which is useful if the teacher wants to set a question and then later use the files to get the students to check their working.
Here are some screenshots, click to enlarge