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If A=[{:(1,2),(4,1):}] , then find A^(2)...

If `A=[{:(1,2),(4,1):}]` , then find `A^(2)+2A+7I`.

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We have, `A=[{:(1,2),(4,1):}]`
`therefore A^(2)=[{:(1,2),(4,1):}][{:(1,2),(4,1):}]`
`=[{:(1+8,2+2),(4+4,8+1):}]=[{:(9,4),(8,9):}]`
`therefore A^(2)+2A+7I=[{:(9,4),(8,9):}]+[{:(2,4),(8,2):}]+[{:(7,0),(0,7):}]=[{:(18,8),(16,18):}]`
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