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Question
If A = `[[ab,b^2],[-a^2,-ab]]` , show that A2 = O
Solution
Given : A= `[[ab b^2],[-a^2 -ab]]`
Now,
`A^2=A A`
`⇒A^2= [[ab b^2],[-a^2 -ab]] [[ab b^2],[-a^2 -ab]]`
`⇒A^2=[[a^2b^2-a^2b^2 ab^3-ab^3],[-a^3b+a^3b -a^2b^2+a^2b^2]]`
`⇒A^2[[0 0],[0 0]]`
`⇒A^2= 0`
Hence proved.
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