If the adjoint of a 3 × 3 matrix P is 1 2 1 4 1 1 4 7 3 , then the possible value(s) of the determinant of P is (are)

Question

If the adjoint of a 3 × 3 matrix P is ​ 1 2 1 ​ 4 1 1 ​ 4 7 3 ​ ​ , then the possible value(s) of the determinant of P is (are)

TestHub · Accepted Answer

We know for a third order matrix P , ∣ Adj P ∣ = ∣ P ∣ 2 Where ∴ ​ ∣ Adj P ∣ = 1 ( 3 − 7 ) − 4 ( 6 − 7 ) + 4 ( 2 − 1 ) = 4 ∣ P ∣ 2 = 4 P ∣ P ∣ = 2 or − 2 ​

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