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Question

If ∣ ∣ ∣1xx2xx21x21x∣ ∣ ∣=3, then find the value of ∣ ∣ ∣x310xx40xx4x31xx4x310∣ ∣ ∣

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Solution

Let D=|A|=∣ ∣ ∣1xx2xx21x21x∣ ∣ ∣=3
Determinant of co-factors
Dc=∣ ∣ ∣x310xx40xx4x31xx4x310∣ ∣ ∣
Dc=|adjA| Since, |A|=|AT|
Dc=|A|2=9
∣ ∣ ∣x310xx40xx4x31xx4x310∣ ∣ ∣=9

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