What is the transpose of a (1,1) tensor? If we define a matrix to be an array of numbers, the transpose flips the array along the diagonal.

Let's talk about the Planck mass. Here is the action for four-dimensional gravity coupled to matter. Varying the action with respect to the metric gives the Einstein field equations. Classically, the overall normalization of the action does not matter: it would amount to multiplying both sides by the same constant.