Start Maple from Start Menu/Program Files/ or using the icon
in f:\math115

Load the linear algebra progams with the command:
>    with(linalg);

Every Maple command must end with a semi-colon ";"

We can create matrices by using the following command
>    A:=matrix(2,3,[1,-1,2,3,0,1]);

Note that we use ":=" to assign a value to A. 

Next we create a random matrix B, with entries between -7 and +7
>    B:=randmatrix(2,3,entries=rand(-7..7));

We can add these matrices together using the command "matadd"
>    C:=matadd(A,B);

If you want to know more about a Maple command, type
>    ?matadd
to exit from the help page, close the subwindow, or use the 
Window menu to move between them.

Use the help to find out how to use matadd to get 3A - 2B

Check that matadd(B,A) is the same as C

Evaluate the scalar multiple
    F:=-1*A;
To give the actual values in the matrix, we use 
    evalm(F);
Check what you get when you add F to A.

We can take the transpose of any matrix with "transpose",
try 
>  transpose(A)
and see that the same numbers show up, just that rows 
become columns and vice versa

Check that transpose(C) = matadd(transpose(A),transpose(B))
and also predict and check what the transpose of 3A - 2B will be.

We will, of course, multiply matrices, the command is "multiply".
Try multiplying A and B, then try to find the relationship 
between the product of A, transpose(B), B and transpose(A).

Create two random 3x3 matrices J and K and multiply them first 
as J times K and then and K times J. Are the results the same matrix? 

Try to find a pair of matrices for which this relationship gives 
the opposite result, so you have JK not equal to KJ 
and GH equal to HG or vice versa.