(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

2. Relevant equations

3. The attempt at a solution

Det( ## e^A ## ) = ## e^{(trace A)} ##

## trace(A) = trace( SAS^{-1}) = 0 ## as trace is similiarity invariant.

Det( ## e^A ## ) = 1

The answer is option (a).

Is this correct?

But in the question, it is not given that S AS^{-1}is a similarity matrix of A. I assumed it without checking.

So, should I check it by calculating eigen values of both S and ## SAS^{-1}## and their eigen vectors?

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# Determinant of exponential matrix

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