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0 If I created a GPG public key with an expiration after 10 years and later I wanted to reduce it to 5 years, is it possible? Also, if I already published the key to a key server, how to make changes there? gnupg share | improve this question asked Jan 6 at 20:41 Thinker migrated from security.stackexchange.com Jan 6 at 20:52 This question came from our site for information security professionals. ...

1 $begingroup$ I'm having trouble proving this without using determinants. I know how to prove it with the product of just two matrices, but I'm not sure how to generalize this to a product of k matrices. Is there a way to do this proof without determinants? To clarify the question, each matrix is an $n$ by $n$ matrix. For example, I know that if the determinant of the product is nonzero, then all of the determinants of the individual matrices must also be nonzero. I also know that if a product of two matrices $A$ and $B$ , $AB$ is nonsingular, then there exists a matrix $C$ so that $C(AB) = I$ and $(AB)C = I$ , and so $(CA)B = I$ and $A(BC) = I$ , so $A$ and $B$ are both invertible, and thus nonsingular. I'm looking for a way to generalize this. Or just any other way to prove this with...