Let x,y,z > 1 and A = [ 1 log x y log x z log y x 2 log y z log z x log z y 3 ]. Then |adj~(adj~A²)| is equal to

Matrices and Determinants: JEE Main 2023 Mathematics question

JEE Main 2023 · 25 Jan, Morning shift · Q4540

JEE Main 202325 Jan, Morning shiftMathematicsMediumMatrices and Determinants245× since 2002

Let

x,y,z > 1

and

A = \left[ {\matrix{ 1 & {{{\log }_x}y} & {{{\log }_x}z} \cr {{{\log }_y}x} & 2 & {{{\log }_y}z} \cr {{{\log }_z}x} & {{{\log }_z}y} & 3 \cr } } \right]

. Then

\mathrm{|adj~(adj~A^2)|}

is equal to

JEE Main 2023 · 25 Jan, Morning shift · Q4540

JEE Main 202325 Jan, Morning shiftMathematicsMediumMatrices and Determinants245× since 2002

Let

x,y,z > 1

and

A = \left[ {\matrix{ 1 & {{{\log }_x}y} & {{{\log }_x}z} \cr {{{\log }_y}x} & 2 & {{{\log }_y}z} \cr {{{\log }_z}x} & {{{\log }_z}y} & 3 \cr } } \right]

. Then

\mathrm{|adj~(adj~A^2)|}

is equal to