How to Find the Trace of ABA^-1 in Component Form?

sarrfriend
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Let A, B be matrices with components Aμν , Bμν such that μ, ν = 0, 1, 2, 3. Indices are lowered and raised with the metric gμν and its inverse gμν. Find the trace of ABA-1 in component form?
Since A and B are generalized versions of tensors, finding their inverse becomes very tedious if we try to solve this by brute force, isn't it? Is there an easier way to find the solution?
 
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welcome to pf!

hi sarrfriend! welcome to pf! :smile:

hint: tr(ABC) - tr(CAB) = … ? :wink:​
 
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