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

Question

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

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

Monjur Alahi

4 views

2025-01-04 04:42

1 Answers

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Salim Ahmed Kawsar · Accepted Answer · 2023-02-05T15:29:48+06:00

Salim Ahmed Kawsar

Correct Answer - 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)]`

4 views Answered 2023-02-05 15:29