Problem9:Use the result of the previous problem to find the inverse of the matrix, 
> ;
[ 1 1 0 0] [ ] [1 1 0 0] [ ] [ 1 1 1 1] [ ] [ 1 1 1 1]

We partition the matrix into, 
> ;
[A 0] [ ] [B A]
where, 
> A := matrix(2,2,[1,1,1,1]); B := matrix(2,2,[1,1,1,1]);
[ 1 1] A := [ ] [1 1] [1 1] B := [ ] [1 1]
as it was seen in Problem8 the inverse is also partitioned into 4 blocks with the inverse of A in the main diagonal, 0 on the upper right hand side and C in the lower left hand side. The matrix C is given by, 
> C :=  inverse(A) &* B &* inverse(A);
//[1/2 1/2] \ [1/2 1/2]\ C := [ ] &* B &* [ ] \\[1/2 1/2 ] / [1/2 1/2 ]/> evalm(C);
[ 0 0] [ ] [1 0]
Thus, the inverse of the original 4x4 matrix is, 
> ;
[1/2 1/2 0 0 ] [ ] [1/2 1/2 0 0 ] [ ] [ 0 0 1/2 1/2] [ ] [1 0 1/2 1/2 ]