# Thread: A problem of algebraic complement

1. ## A problem of algebraic complement

Assume the matrix of order n is : $A = \left(\begin{array}{ccc}a_{11}&...&a_{1n}\\...&... &...\\a_{n1}&...&a_{nn}\end{array}\right)$

and we have: $\sum_{j=1}^{n}a_{ij} = \sum_{j=1}^{n}a_{ji} = 0,i = 1,2,...,n.$

show that: all the algebraic complement(the number of algebraic complements is $n^{2}$ ) of $A$ are equal.

2. Originally Posted by Xingyuan
Assume the matrix of order n is : $A = \left(\begin{array}{ccc}a_{11}&...&a_{1n}\\...&... &...\\a_{n1}&...&a_{nn}\end{array}\right)$

and we have: $\sum_{j=1}^{n}a_{ij} = \sum_{j=1}^{n}a_{ji} = 0,i = 1,2,...,n.$

show that: all the algebraic complement (the number of algebraic complements is $n^{2}$ ) of $A$ are equal.
... and "algebraic complement of a matrix" means what?