This preview shows page 1. Sign up to view the full content.
Solution:
To prove:
If A be a square matrix with integer entries, that is
aijϵZ
for all
,
i j
, then A has an inverse
with integer entries if and only if
( ) = ±
det A
1
Proof:
Let’s assume a system of linear equations given by:
=
Ax b
where matrix
A
has integer values and
also assume that
b
is integer.
Now, by Cramer’s rule:
=
……………………[ ]
xi detAidetA
1
Where,
detAi
is the determinant of the matrix
This is the end of the preview. Sign up
to
access the rest of the document.
 Spring '11
 Prof.Ramachandran

Click to edit the document details