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Let P, Q and R be invertible matrices of...

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 _______.

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The correct Answer is:
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`
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