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Question
If f (x) = x2 − 2x, find f (A), where A=
Solution
Given ; `f(x)=x^2-2x`
`f(A)=A^2-2A` Now
`A^2=A A`
`⇒A^2=[[0,1,2],[4,5,0],[0,2,3]] [[0,1,2],[4,5,0],[0,2,3]]`
`⇒A^2=[[0+4+0,0+5+4,0+0+6],[0+20+0,4+25+0,8+0+0],[0+8+0,0+10+6,0+0+9]]`
`⇒A^2=[[4,9,6],[20,29,8],[8,16,9]]`
`f(A)=A^2-2A`
⇒f(A)= `[[4,9,6],[20,29,8],[8,16,9]]-2` `[[0,1,2],[4,5,0],[0,2,3]]`
⇒f(A)= `[[4,9,6],[20,29 ,8],[8,16,9]]-` `[[0,2,4],[8,10,0],[0,4,6]]`
⇒f(A)= `[[4-0,9-2,6-4],[20-8,29-10,8-0],[8-0,16-4,9-6]]`
⇒f(A)= `[[4,7,2],[12,19,0],[8,12,3]]`
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