Exercise 111.64.7 (Injectives). Let $(A, \mathfrak m, \kappa )$ be an Artinian local ring. Assume $A$ is injective as an $A$-module. Show that $\mathop{\mathrm{Hom}}\nolimits _ A(\kappa , A)$ has dimension $1$ has a $\kappa $-vector space.

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