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Question
If A = `[[1 1],[0 1]]` show that A2 = `[[1 2],[0 1]]` and A3 = `[[1 3],[0 1]]`
Solution
Given : A= `[[1 1],[0 1]]`
Now,
`A^2=A A`
`A^2=[[1 1],[0 1]]` `[[1 1],[0 1]]`
`A^2=[[1+0 1+1],[0+0 0+1]]`
`⇒A^2=[[1 2],[0 1]]`
`A^2=A^2A`
`A^2=[[1 2],[0 1]] [[1 1],[0 1]]`
`⇒A^3= [[1+0 1+2],[0+0 0+1]]`
`A^3=[[1 3],[0 1]]`
Hence proved.
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