Multiplying matrices is a part of life. At least, it is a part of life for the advanced math student. While it is terribly important to understand how to do this the old fashioned pencil and paper way, one can use a graphing calculator also. It may take a little while to figure out how to do it, but with a little practice, using a graphing calculator can really speed up the process.
Not all graphing calculators are the same, but most students, professionals, schools, etc. use some manner of Texas Instruments model of graphing calculator. Most of these work mostly the same, but the following directions are geared toward the TI-83 Plus. (These will most likely work for TI - 82, TI - 83, TI - 84, and many other models.)
First, the two matrices to be multiplied need to be input. Don't forget that the size of the two matrices must be paired up properly. Namely, the number of columns of the first matrix must match the rows of the second, and the number of rows of the first matrix must mach the columns of the second. In order to put numbers into a Matrix, press the "2nd" button, followed by the "x-1" button. This will open up the Matrix Menu. Arrow over to the "Edit" heading, and select which Matrix to edit. (Using A first, then B is typically the best and easiest way.) Press "enter" on the selected matrix. At the top of the screen, the size of the matrix can be adjusted by typing in numbers where the dimensions are displayed. Once that has been selected, arrow to the different locations within the matrix to input the numbers. Repeat this process for the second matrix.
Once the two matrices are set up properly, it just comes down to the last step, multiplying. Call up the Matrix Menu again, and select the first matrix. Press the multiply button. Go back to the Matrix Menu and select the second matrix. Press enter, and watch the newly created product matrix be displayed on the screen. Note that any two properly sized matrices can also be added or subtracted in this method. Though, in most cases, it is easier to add and subtract matrices by hand.