Let AMnnQ be a matrix satisfying the condition that if vQn i

Let AMn×n(Q) be a matrix satisfying the condition that if vQn is a vector all of the components of which are nonnegative, then all of the components of Av are nonnegative. Are all of the entries in A necessarily nonnegative?

Solution

No,it\'s not necessary that all the entries of matrix A had to be non negative. The only thing to keep in mind is that while multiplying A with n all entries should be positive.

i.e., An must be positive