Positive definite and semi definite in non linear programming

Question

How can I prove the following.
Suppose that A is a square matrix and suppose that there is another matrix B such that $A=B^TB$.

a)Show that A is positive semi definite

b)Show that if B has full column rank then A is positive definite.

Answer 1

To part (a), $z^TB^TBz$ is the sum of the squares of the entries in $Bz$.