Let A be the set of all non-singular n × n real matrices, for some fixed n ≥…
GATE · 1995 · CS · Question 2 subpartsModified — slightly modified from the official paper; see the solution
Let A be the set of all non-singular n × n real matrices, for some fixed n ≥ 2, and let * be the matrix multiplication operation. Then ⟨A, *⟩ is:
- A.
A is closed under * but ⟨A, *⟩ is not a semigroup.
- B.
⟨A, *⟩ is a semigroup but not a monoid.
- C.
⟨A, *⟩ is a monoid but not a group.
- D.
⟨A, *⟩ is a group but not an abelian group.
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