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Let P=[(1,2,1),(0,1,-1),(3,1,1)]. If the...

Let `P=[(1,2,1),(0,1,-1),(3,1,1)]`. If the product PQ has inverse `R=[(-1,0,1),(1,1,3),(2,0,2)]` then `Q^(-1)` equals

A

`[(3,2,9),(-1,1,1),(0,1,8)]`

B

`[(5,2,9),(-1,1,1),(0,1,7)]`

C

`[(2,-1,0),(10,6,3),(8,6,4)]`

D

none of these

Text Solution

Verified by Experts

The correct Answer is:
C
`(PQ)^(-1)=R`
`implies Q^(-1)xxP^(-1) =R`
`implies Q^(-1) =RP=[(-1,0,1),(1,1,3),(2,0,2)][(1,2,1),(0,1,-1),(3,1,1)]`
`=[(2,-1,0),(10,6,3),(8,6,4)]`
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