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If A=[(1,2,3),(-1,1,2),(1,2,4)], then (A...

If `A=[(1,2,3),(-1,1,2),(1,2,4)]`, then `(A^(2)-5A)A^(-1)=`

A

`{:[(4,2,3),(-1,4,2),(1,2,1)]:}`

B

`{:[(-4,2,3),(-1,-4,2),(1,2,-1)]:}`

C

`{:[(-4,-1,1),(2,-4,2),(3,2,-1)]:}`

D

`{:[(-1,-2,1),(4,-2,-3),(1,4,-2)]:}`

Text Solution

Verified by Experts

The correct Answer is:
B
WE have,
`A={:[(1,2,3),(-1,1,2),(1,2,4)]:}`
Now, `(A^(2)-5A)A^(-1)`
`=A^(2)*A^(-1)-5A*A^(-1)=A-5l`
`{:[(1,2,3),(-1,1,2),(1,2,4)]:}-{:[(5,0,0),(0,5,0),(0,0,5)]:}`
`={:[(-4,2,3),(-1,-4,2),(1,2,-1)]:}`
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