Explaining the answer step by step would be much appreciated.

16.2 Let Q(x) x"Ax be a quadratic form on R". By evaluating ( on cach of the coordinate axes in R", prove that a necessary condition for a symmetric matrix to be positive definite (positive semidefinite) is that all the diagonal entries be positive (nonnegative). State and prove the corresponding result for negative and negative semidefinite matrices. Give an example to show that this necessary condition is not sufficient