Let x, y, z1 and A=[1 log x y log x z log y x 2 log y z log z x log z y 3]. Then mid operatornameadj( operatornameadj A2. )| is equal to

Question

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 mid operatornameadj( operatornameadj A2. )| is equal to (A) 48 (B) 28 (C) 24 (D) 64

Tardigrade Admin · Accepted Answer

|A|=(1/ log x ⋅ log y ⋅ log z) | log x log y log z log x 2 log y log z log x log y 3 log z|=2 ⇒| operatornameadj( operatornameadj A2)|=|A2|4=28

Q. Let $x, y, z > 1$ and $A = ⎣ ⎡ 1 lo g_{y} x lo g_{z} x lo g_{x} y 2 lo g_{z} y lo g_{x} z lo g_{y} z 3 ⎦ ⎤$ . Then $∣ adj (adj A^{2}) ∣$ is equal to

$4^{8}$

$2^{8}$

$2^{4}$

$6^{4}$

$∣ A ∣ = \frac{1}{l o g x \cdot l o g y \cdot l o g z} ∣ ∣ lo g x lo g x lo g x lo g y 2 lo g y lo g y lo g z lo g z 3 lo g z ∣ ∣ = 2$
$\Rightarrow ∣ ∣ adj (adj A^{2}) ∣ ∣ = ∣ ∣ A^{2} ∣ ∣^{4} = 2^{8}$

Q. Let x,y,z>1 and A=⎣⎡​1logy​xlogz​x​logx​y2logz​y​logx​zlogy​z3​⎦⎤​. Then ∣adj(adjA2)∣ is equal to

48

28

24

64