If A ~ B and A has any of the following properties, show that B has the same property. (a)

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If A ~ B and A has any of the following properties, show that B has the same property.
(a) Idempotent, that is A2 = A.
(b) Nilpotent, that is Ak= 0 for some k ≥.
(c) Invertible

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Question Posted: June 21, 2016 06:39:59