If A, is a covariant vector field, show that A,A,, is a skew-symmetric second rank tensor field. Suppose that BA, is an invariant for an arbitrary contravariant vector B. Show A transforms like a covariant vector. Show that A-AA- A where A, is a covariant vector. o Suppose that. B'B' A,, is an invariant for an arbitrary contravariant vector B. Show that A) (that is, the symmetric part of A) is a second rank covariant tensor. If A, is a skew-symmetric covariant tensor, verify that Bijk - Ajk+Aki + Aski transforms as a tensor.