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Multiplicative inverse of the matrix [[2...

Multiplicative inverse of the matrix `[[2,1],[7,4]]` is (i) `[[4,-1],[-7,-2]]` (ii) `[[-4,-1],[7,-2]]` (iii) `[[4,-1],[7,2]]` (iv) `[[4,-1],[-7,2]]`

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The correct Answer is:
N/a
`Let A=[{:(2,1),(7,4):}]`
`Now , A=IA`
`implies [{:(2,1),(7,4):}]=[{:(1,0),(0,1):}]A`
`implies [{:(1,(1)/(2)),(7,4):}]=[{:((1)/(2),0),(0,1):}] R+_(1)to (1)/(2)R_(1)`
`implies [{:(1,(1)/(2)),(0,(1)/(2)):}]=[{:((1)/(2),0),((-7)/(2),1):}]AR_(2)to R_(2)-7R_(1)`
`implies [{:(1,(1)/(2)),( 0,1)=[{:((1)/(2)),(0,1):}]=[{:((1)/(2),0),(-7,2):}]AR_(2)to 2R_(2)`
`implies [{:(1,0),(0,1):}]=[{:(4,-1),(-7,2):}]AR_(1)to R_(1)-(1)/(2)R_(2)`
`therefore A^(-1)=[{:(4,-1),(-7,2):}]`
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