(a) Sis a ring. a (b) (6 b)* - (** i). 0 where denotes some integer. Also find the idempotents and nilpotent elements of S. Show that nilpotent elements form a subring.

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Chapter2: Second-order Linear Odes
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6.
Let S be the set of 2 × 2 matrices over Z of the form (?). Show
that
(a) S is a ring.
(b)
(a b)* = (a* .*).
0
0
where denotes some integer.
Also find the idempotents and nilpotent elements of S. Show that
nilpotent elements form a subring.
Transcribed Image Text:6. Let S be the set of 2 × 2 matrices over Z of the form (?). Show that (a) S is a ring. (b) (a b)* = (a* .*). 0 0 where denotes some integer. Also find the idempotents and nilpotent elements of S. Show that nilpotent elements form a subring.
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