Q2.17

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Let $A$ be the set of all non-singular matrices over real number and let $*$ be the matrix multiplication operation. Then

(A)

$A$ is closed under $*$ but $\langle A, *\rangle$ is not a semigroup.

(B)

$\langle A, *\rangle$ is a semigroup but not a monoid.

(C)

$\langle A, * \rangle$ is a monoid but not a group.

(D)

$\langle A, *\rangle$ is a a group but not an abelian group.

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