(a) Show that the set $M_2 (Z)$ of all $2 \times 2$ matrices over int…
Previous year question for Discrete Mathematics.
Question
(a) Show that the set $M_2 (Z)$ of all $2 \times 2$ matrices over integers is an abelian group under addition of matrices.
(b) Prove that a non-empty subset $H$ of a group $G$ is a subgroup of $G$ if and only if
(i) $ab \in H \quad \forall a, b \in H$
(ii) $a^{-1} \in H \quad \forall a \in H$
(c) Prove that $(2n + 7) < (n + 3)^2$ by using the principle of mathematical induction for all $n \in \mathbb{N}$.
- Year: 2018
- Subject: Discrete Mathematics