If I have A^ alpha beta B_ beta gamma then this should be the equivalent to the following matrix multiplication: AB since we're summing over the columns of A and the rows of B. By the same logic, if I have A^ alpha beta B_ gamma alpha then this is BA in matrix notation. But what if I was doing A^ alpha beta B_ alpha gamma? Would that be equivalent to AᵗB or Bᵗ A in matrix notation or something else entirely? Furthermore, What would my index notation look like for the resultant? Would it look something like C^ beta_ gamma, or would one index be further to the left than the other?