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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
asked in Set Theory & Algebra by Active (2.6k points)
edited by | 60 views
option b ?
Answer given is C. You can anyways explain your choice of option.
Monoid means there is an identity element which in this case should be identity matrix. So I think it should be a Monoid
It should be a group.

As the inverse of an upper triangular matrix is always upper triangular and exists when all diagonals are non zero.

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