Why Doesn't the Tensor Identity Work Out?

[QuickLoris]

My textbook (regarding continuum mechanics) has the following identity that is supposed to be true for all tensors:

a$\cdot$Tb = b$\cdot$T^Ta

But I don't get the same result for both sides when I work it out.
For each side, I'm doing the dot product last. For example, I compute Tb first and then computer the dot product of a$\cdot$Tb. Is that right? I tried doing it the other way around also, but it didn't work out that way either.

I'm still pretty new to this subject and teaching it to myself, so I figure I'm multiplying something incorrectly, but I don't understand what.

 

[afreiden]

My textbook (regarding continuum mechanics) has the following identity that is supposed to be true for all tensors:

a$\cdot$Tb = b$\cdot$T^Ta

But I don't get the same result for both sides when I work it out.

I don't know what you might be doing wrong, but vector algebra is commutative, as you say.

For each side, I'm doing the dot product last. For example, I compute Tb first and then computer the dot product of a$\cdot$Tb. Is that right?

The original identity is definitely correct, as it is a common one used as a starting point for other math proofs.