1: Show that if A is a positive definite 2 x 2 matrix,

(1) $a_{11} + a_{22} - 2a_{12} > 0$,

(2) $a_{11} + a_{22} + 2a_{12} > 0$,

(3) $a_{22}(a_{11} + a_{22} - 2a_{12}) > (a_{12} - a_{22})^2$.