Let $A\,\,{\rm{be}}\,\,{\rm{a}}\,3 \times 3\,$ matrix such that $adj\,A\, = \,\left[ {\begin{array}{*{20}{c}} 2&{ - 1}&1\\ { - 1}&0&2\\ 1&{ - 2}&{ - 1} \end{array}} \right]\,\,{\rm{and}}\,B = \,\,{\rm{adj}}\,\,{\rm{(adj}}\,A{\rm{)}}\,$ ${\rm{If}}\,\left| A \right|\,{\rm{ = }}\,\lambda \,{\rm{and}}\,\left| {{{({B^{ - 1}})}^T}} \right|\,{\rm{ = }}\,\mu, $ then the ordered pair, $\,\left( {\left| \lambda \right|,\,\mu } \right)$ is equal to

$\left( {9,\,\frac{1}{{81}}} \right)$

$\left( {9,\,\frac{1}{9}} \right)$

JEE MATHEMATICS MCQ: MATRICES

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Application +4 | -1

Let

A\,\,\mathrm{be}\,\,\mathrm{a}\,3 \times 3\,

matrix such that

adj\,A\, = \,\left[ {\begin{array}{cccccccccccccccccccc} 2&{ - 1}&1\\ { - 1}&0&2\\ 1&{ - 2}&{ - 1} \end{array}} \right]\,\,\mathrm{and}\,B = \,\,\mathrm{adj}\,\,\mathrm{(adj}\,A\mathrm{)}\,

\mathrm{If}\,\left| A \right|\,\mathrm{ = }\,\lambda \,\mathrm{and}\,\left| {{{({B^{ - 1}})}^T}} \right|\,\mathrm{ = }\,\mu,

then the ordered pair,

\,\left( {\left| \lambda \right|,\,\mu } \right)

is equal to

View answer and explanation

Correct option: D

\left( {3,\,\frac{1}{{81}}} \right)

Option D

\left( {3,\frac{{1}}{{81}}} \right)

is correct because by using the properties of adjoint and determinant of a matrix, we can find the values of |λ| and μ.