Solution
= Solution
Contracting one index from each tensor means summing them, for example $C_{i_1\ldots i_{p-1}j_1\ldots j_{q-1}}=A_{i_1\ldots i_{p-1}r}B_{rj_1\ldots j_{q-1}}$. Its rank is $p+q-2$. Substitution of the transformation laws for $p=q=3$ and $R_{rs}R_{rt}=\delta_{st}$ proves the tensor law.