(a) Given the components of a (20) tensor Mαβ as the matrix

find:
(i) The components of the symmetric tensor M(αβ) and the antisymmetric tensor M[αβ];
(ii) The components of Mαβ;
(iii) The components of Mαβ;
(iv) The components of Mαβ .
(b) For the (11) tensor whose components are Mαβ, does it make sense to speak of its symmetric and antisymmetric parts? If so, define them. If not, say why.
(c) Raise an index of the metric tensor to prove
ηαβ = (α(.

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