J Matrix has determinant d

>> J = [ d l ; 0 1]

J =

[ d, l]
[ 0, 1]

>> det(J)

ans =

d

>> J = [d,d,l;
0 1 0;
0 0 1]

J =

[ d, d, l]
[ 0, 1, 0]
[ 0, 0, 1]

>> det(J)

ans =

d

>> J = [d,d,d ,l;0,1,0,0; 0,0,1,0; 0,0,0,1]

J =

[ d, d, d, l]
[ 0, 1, 0, 0]
[ 0, 0, 1, 0]
[ 0, 0, 0, 1]

>> det(J)

ans =

d

========== Inverses ==============

d

>> inv(J)

ans =

[ 1/d, -1, -1, -l/d]
[   0,  1,  0,    0]
[   0,  0,  1,    0]
[   0,  0,  0,    1]

>> J = [d,d,l;0,1,0;0,0,1]

J =

[ d, d, l]
[ 0, 1, 0]
[ 0, 0, 1]

>> inv(J)

ans =

[ 1/d, -1, -l/d]
[   0,  1,    0]
[   0,  0,    1]

>> det(inv(J))

ans =

1/d