Question: Problem : A group of nonsingular matrices include AB and A^(-1) if it includes A and B. Products and inverses stay in the group. Which

Problem : A group of nonsingular matrices include AB and A^(-1) if it includes A and B. "Products and inverses stay in the group." Which of these are groups?

(1) All exponentials e^(tA) of a fixed matrix A.

(2) Matrices P with positive eigenvalues

I can't solve this problem. the solution is, (1) can be the group and (2) can't be the group.

why can (1) be the group, and why cannot (2) be the group???

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