Proving Tensor Commutation: T^abc S_b vs S_b T^abc

[Irid]

Homework Statement

How would you show that

$T^{abc}S_{b} = S_{b}T^{abc}$

but

$T^{abc} S_{bd} \neq S_{bd} T^{abc}$

in general?

The Attempt at a Solution

If I write out the sums explicitly, they appear totally the same to me. Any hints or ideas please?

 

[dextercioby]

You must be joking, right ? If T and S are commutative variables (Grassmann parity =1), then it doesn't matter in which order you write those two sums.