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I am doing some exercises in continuum mechanics and it is a little bit confusing. I am given the following equations ## A_{ij}= \delta_{ij} +au_{i}v_{j} ## and ## (A_{ij})^{-1} = \delta_{ij} - \frac{au_{i}v_{j}}{1-au_{k}v_{k}}##. If I want to take the product to verify that they give the identity matrix (its components maybe is more accurate), should I change in one of the expressions the index letters and proceed(change the free indices I mean)? Is this the correct approach ## (\delta_{ij} +au_{i}v_{j})(\delta_{mn} - \frac{au_{m}v_{n}}{1-au_{k}v_{k}}) ## and do the calculations? Does this term make sense ## \delta_{ij}\delta_{mn}##?

Thanks lot