Start Maple from Start Menu/Program Files/ or using the icon
in f:\math115, or double click on 115lab2base.mws

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

If you end a Maple command with a colon ":" it doesn't show output

Form the 3x3 zeroes matrix and see what Maple says when it has no inverse.
>    Z:=matrix(3,3,0);
The new command you will need is 
>    inverse(Z);

Generate several 2x2 matrices and find two whose inverses do exist.

Multiply these inverses and check that the relation for the
inverse of a product is the product of the inverses in the other order.
Check this relation still holds for three of your matrices multiplied.

Check that there is no easy relation between inverse(A+B) and the inverses
Find two matrices C and W such that C and W have inverses but (C+W) doesn't
(note that we can't use D as a variable as it is used for differentiation)

We can also do row operations on matrices with Maple.
>  E:=matrix(3,4,[1,3,-1,5,-2,1,-5,4,0,-1,1,-2]);

the commands we will use will be "addrow", "mulrow" and "swaprow".
Perform Gaussian Elimination on E and verify that it has rank 2 by typing
>  rank(E);
We can also find the row reduced echelon form with the command "rref"

Create a random 4x4 matrix F with entries between -1 and 2 and make sure that
rank(F) = 4. 
We will now solve the matrix equation 
       F[x1 x2 x3 x4]^T = matrix(4,1,[5,-1,3,2]);
First solve it by using "augment" 
>  F1:=augment(F,matrix(4,1,[5,-1,3,2]));
and row reductions on F1 by hand, then use the 
command "pivot" to do it column by column, then "rref" to check directly.

We can also solve by using
>   linsolve(F,matrix(4,1,[5,-1,3,2]));
or 
>   backsub(gausselim(F1));
or
>   rref(F1);

We can also use row operations to find inverses, if we take the matrix
>   J:=matrix(3,3,[-1,-2,2,1,-2,-1,-1,1,1]);
and augment to it the 3x3 identity matrix which we can get using 
>   Ij:=diag(1,1,1);
and
>   K:=augment(J,Ij);

If we then apply rref to this, the inverse appears...
Use one of the methods above for this and check your answer with inverse(J)