Consider the set H of all 3 × 3 matrices of the type:
$\begin{bmatrix} a&f&e\\ 0&b&d\\ 0&0&c\\ \end{bmatrix}$
where a, b, c, d, e and f are real numbers and $abc ≠ 0$. Under the matrix multiplication operation, the set H is:
(a) a group
(b) a monoid but not a group
(c) a semigroup but not a monoid
(d) neither a group nor a semigroup