Consider the set H of all 3 × 3 matrices of the type where a, b, c, d, e and f…

GATE · 2005 · CS

Consider the set H of all 3 × 3 matrices of the type 

where a, b, c, d, e and f are real numbers and abc ≠ 0. Under the matrix multiplication operation, the set H is 

1. A.

   a group
   

2. B.

   a monoid but not a group
   

3. C.

   a semigroup but not a monoid
   

4. D.

   neither a group nor a semigroup
   

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