Let P, Q and R be invertible matrices of order 3 such `A=PQ^(-1), B=QR^(-1)` and `C=RP^(-1)`. Then the value of det. `(ABC+BCA+CAB)` is equal to _____

Question

Let P, Q and R be invertible matrices of order 3 such `A=PQ^(-1), B=QR^(-1)` and `C=RP^(-1)`. Then the value of det. `(ABC+BCA+CAB)` is equal to _____

Let P, Q and R be invertible matrices of order 3 such `A=PQ^(-1), B=QR^(-1)` and `C=RP^(-1)`. Then the value of det. `(ABC+BCA+CAB)` is equal to _______.

Monjur Alahi

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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 - 27
We have `A=PQ^(-1), B=QR^(-1), C=RP^(-1)`
`:. ABC=I, BCA=I, CAB=I`
`:.` det. `(ABC+BCA+CAB)=` det. `(3I)=3^(3)xx` det. `(I)=27`

5 views Answered 2023-02-05 15:29