Paper 3, Section I, C

What does it mean for a second-rank tensor $T_{i j}$ to be isotropic? Show that $\delta_{i j}$ is isotropic. By considering rotations through $\pi / 2$ about the coordinate axes, or otherwise, show that the most general isotropic second-rank tensor in $\mathbb{R}^{3}$ has the form $T_{i j}=\lambda \delta_{i j}$, for some scalar $\lambda$.

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