Based on the operations allowed between Tensors, indicate whether the following expressions are well defined and determine the type and range of the tensor that results:

$A_{}{B}_{}{C}^{}$

$S^{}-\frac{3}{4}{A}_{}^{}$

$2A_{}+S_{}{A}^{}+B_{}$

$S^{}{T}_{}^{}{A}_{}$

$A^{}{C}_{}$

EXAMPLES

$A_{}{B}^{}=C_{}^{}$: yes, rank $2$ mixed type

$S^{}+3F^{}$: It is NOT defined.

$-A_{}+S_{}{A}^{}$: yes, rank $1,$ covariant type.

$-S^{}{C}_{}^r=$ yes, rank $4,$ mixed.