1. The problem statement, all variables and given/known data I have several problems that ask me to prove that some quantity "transforms like a tensor" For example: "Suppose that for each choice of contravariant vector (a vector) A^nu(x), the quantities B_mu(x) are defined at teach point through a linear relationship of the form B_mu(x) =T_mu_nu(x) A^nu(x) transform like a covariant vector (1-form). Prove that the quantities T_mu_nu(x) transform like a tensor of type (0,2) at each point." (Here an underscore followed by a letter is a lower index and a caret followed by a letter is an upper index). 2. Relevant equations Transformation property of a tensor: T'_mu_nu = dx^mu/dx'^mu dx^nu/dx'^nu T_mu_nu (dx is a partial derivative and) 3. The attempt at a solution My first guess is that I need to apply a coordinate transformation to both sides of the equation given in the problem, but I'm kind of stuck there. I don't know how to manipulate things to get T_mu_nu by itself and show it obeys the tensor transformation property.