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Matrices and Determinants question

2021 · Shift 1 · Q30
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  5. /2021 · Shift 1 · Q30

Matrices and Determinants question

2021 · Shift 1 · Q30

JEE AdvancedMathematicsMatrices and DeterminantsMultiple correct+4 / −2
For any 3 ×\times× 3 matrix M, let | M | denote the determinant of M. Let E=[12323481318]E = \left[ {\begin{matrix} 1 & 2 & 3 \\ 2 & 3 & 4 \\ 8 & {13} & {18} \\ \end{matrix} } \right]E=​128​2313​3418​​, P=[100001010]P = \left[ {\begin{matrix} 1 & 0 & 0 \\ 0 & 0 & 1 \\ 0 & 1 & 0 \\ \end{matrix} } \right]P=​100​001​010​​ and F=[13281813243]F = \left[ {\begin{matrix} 1 & 3 & 2 \\ 8 & {18} & {13} \\ 2 & 4 & 3 \\ \end{matrix} } \right]F=​182​3184​2133​​ If Q is a nonsingular matrix of order 3 ×\times× 3, then which of the following statements is(are) TRUE?
  1. A
    F = PEP and P2=[100010001]{P^2} = \left[ {\begin{matrix} 1 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & 1 \\ \end{matrix} } \right]P2=​100​010​001​​
  2. B
    | EQ + PFQ −-− 1 | = | EQ | + | PFQ −-− 1 |
  3. C
    | (EF)3 | > | EF |2
  4. D
    Sum of the diagonal entries of P −-− 1EP + F is equal to the sum of diagonal entries of E + P −-− 1FP
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