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Let A be a square matrix of order 3 sati...

Let A be a square matrix of order 3 satisfies the relation `A^(3)-6A^(2)+7A-8I=O` and `B=A-2I`. Also, det. `A=8`, then find the det.B

A

7

B

10

C

29

D

41

Text Solution

Verified by Experts

The correct Answer is:
A
`because B = A -2I `
`therefore A^(-1) B = I - 2A^(-1)` ...(i)
`adj[(B/2)^(-1)]= (B/2)/abs(B/2) = (B/2)/(1/8abs(B)) = (4B)/abs(B) = 4/10 B [because abs(B) = 10 ]`
`= 2/5 B = p/q B` [given]
`therefore p= 2 and q = 5 `
Hence, p + q = 7
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