# determinat value

Printable View

• May 13th 2012, 06:54 AM
saravananbs
determinat value
if A is symmetric matrix of odd order and aii=0 for all i then prove that determinant of A is an even number.

please explain.
• May 15th 2012, 01:12 AM
girdav
Re: determinat value
Has the matrix real entries?
• May 15th 2012, 10:53 AM
saravananbs
Re: determinat value
yes, the entries are integers, other than diagonal elements.
• May 17th 2012, 03:16 AM
girdav
Re: determinat value
We can use the definition of the determinant. Since $a_{ii}=0$, we can sum over the permutations without fixed point. Since these permutations act over a set which have an odd number of elements, these one have a square different from the identity. So you can write the sum as two equal parts, which will give an even number.