For any 3 \times 3 matrix M, let |M| denote the determinant of M. Let E=[\table 1 , 2 , 3 ; 2 , 3 , 4 ; 8 , 13 , 18 ], P=[\table 1 , 0 , 0 ; 0 , 0 , 1 ; 0 , 1 , 0 ] and F=[\table 1 , 3 , 2 ; 8 , 18 , 13 ; 2 , 4 , 3 ] If Q is a nonsingular matrix of order 3 \times 3, then which of the following statements is (are) TRUE? [JEE Adv 2021 P1]

F=P E P and P^{2}=[\table 1 , 0 , 0 ; 0 , 1 , 0 ; 0 , 0 , 1]

E Q+P F Q^{-1}|=|E Q|+P F Q^{-1}|

Sum of the diagonal en tries of P^{-1} E P+F is equal to the sum of diagonal entries of E+P^{-1} F P

Matrices and Determinants

Section: Mathematics

Question : 14 of 56

Marks: +1, -0

For any 3×3 matrix M, let |M| denote the determinant of M. Let E=[

],P=[

] and F=[

]
If Q is a nonsingular matrix of order 3×3, then which of the following statements is (are) TRUE?

[JEE Adv 2021 P1]

F=PEP and P2=[
1 0 0
0 1 0
0 0 1
]
EQ+PFQ−1|=|EQ|+PFQ−1|
|(EF)3|>|EF|2
Sum of the diagonal en tries of P−1EP+F is equal to the sum of diagonal entries of E+P−1FP

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