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if A=[[2,-3],[-4,1]] then adj(3A^2+12A)=...

if `A=[[2,-3],[-4,1]]` then `adj(3A^2+12A)=?`

A

`[(72,-63),(-84,51)]`

B

`[(72, -84),(-63,51)]`

C

`[(51,63),(84,72)]`

D

`[(51, 84),(63,72)]`

Text Solution

Verified by Experts

The correct Answer is:
C
Given `A=[(2,-3),(-4,1)]`
`implies A^(2)=[(2,-3),(-4,1)][(2,-3),(-4,1)]=[(16,-9),(-12,13)]`
`implies 3A^(2)+12A=[(48,-27),(-36,39)]+[(24,-36),(-48,12)]`
`=[(72,-63),(-84,51)]`
adj `(3A^(2)+12A)=[(51,63),(84,72)]`
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