True or False and show the explanations (detailed full process)
1. If A and B are symmetric matrix, then AB is also symmetric.
2. Every vector space possesses a basis
3. Let a=[[(3)/(5)],[(4)/(5)]] and b=[[-(4)/(5)],[(3)/(5)]]. Then {a,b} forms a orthonormal basis
of R^(2)
4. If rank(A)=rank(B),thenrank(A^(2))=rank(B^(2)).