(Solved): 1. Find the following expressions. \( \delta_{j} \) is the Konecker delta, while \( \varepsilon_{i ...

1. Find the following expressions. \( \delta_{j} \) is the Konecker delta, while \( \varepsilon_{i j k} \) is the permutation tensor. a) \( \delta_{i j} \delta_{i j} \) b) \( \delta_{i j} \delta_{j k} \delta_{k p} \delta_{p i} \) c) \( \varepsilon_{i j k} A_{j} A_{k} \) d) \( \delta_{i j} \varepsilon_{i j k} \) e) \( \varepsilon_{m j k} \varepsilon_{n j k} \) (Hint: \( \varepsilon_{i j k} \varepsilon_{i m n}=\delta_{j m} \delta_{k n}-\delta_{j n} \delta_{k m} \) )