Let A, B be second-rank tensors.

(a) Show that A + B is also a second-rank tensor.

(b) Show that A ⊗ B is a fourth-rank tensor.

(c) Show that the contraction of A ⊗ B on its first and fourth slots is a second-rank tensor.

(d) Write the following quantities in slot-naming index notation: the tensor A ⊗ B, and the simultaneous contraction of this tensor on its first and fourth slots and on its second and third slots.