Ideal of an inversable triangular matrix

[karin]

Hello
I need your help please.
I have a block matrix P=[a b ; 0 d], which is inversable.
if f belongs to the ideal of the matrix, how do I prove that
f=$\sum$g$_{ij}$x$_{ij}$
while g$_{ij}$ are regular functions above the space of inversable matrix?
thank you!
Karin

 

[Erland]

I think you should explain the terminology here. What is "the ideal of the matrix", and what are "regular functions above the space of inversable matrix"?