Multiplying a matrix by a scalar (a single number) is a much simpler matter than multiplying a matrix by a matrix. In the example below you just multiply each number in the matrix times 3:
Adding two matrices only requires that they be similarly shaped.
The same is true with subtracting matrices:
You can also combine scalar multiplication with subtraction or addition:
Finally, you can test J versus almost any textbook with Matrix Algebra questions and answers. The problems here are similar to those shown in Kelley’s Algebra, Chapter 9. A great source for Algebra problems is Kelley’s Humongous Book of Algebra Problems. You can also create your own problems using Deal. Here’s how: for a 3 x 3 matrix with numbers no greater than 10, you would use this Deal command with 9?10. You could make some number negative. Then you would assign the matrix (=:) and use the shape command (3 3 $) to make your 3 x 3 matrices. Use J. Play with J.