JEE Mains · Maths · STD 12 - 3 and 4 . metrices and determinant
Let \(\mathrm{A}=\left[\mathrm{a}_{\mathrm{ij}}\right]\) and \(\mathrm{B}=\left[\mathrm{b}_{\mathrm{ij}}\right]\) be two \(3 \times 3\) real matrices such that \(b_{i j}=(3)^{(i+j-2)} a_{j i},\) where \(\mathrm{i}, \mathrm{j}=1,2,3 .\) If the determinant of \(\mathrm{B}\) is \(81,\) then the determinant of \(A\) is
- A \(3\)
- B \(\frac 13\)
- C \(\frac 1{81}\)
- D \(\frac 19\)
Answer & Solution
Correct Answer
(D) \(\frac 19\)
Step-by-step Solution
Detailed explanation
\(\mathrm{b}_{\mathrm{ij}}=(3)^{(i+j-2)} \mathrm{a}_{\mathrm{ij}}\) \(B=\left[\begin{array}{ccc}{a_{11}} & {3 a_{12}} & {3^{2} a_{13}} \\ {3 a_{21}} & {3^2 a_{22}} & {3^3 a_{23}} \\ {3^{2} a_{31}} & {3^{3} a_{32}} & {3^{4} a_{33}}\end{array}\right]\) \(=3^{6}|\mathrm{A}|\)…
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