Question

Let $x, y, z>1$ and $A=\begin{bmatrix}1 & \log _x y & \log _x z \\\ \log _y x & 2 & \log _y z \\\ \log _z x & \log _z y & 3\end{bmatrix}$ Then ∣adj(adj A 2)∣ is equal to

• A. $4^8$
• B. $2^8$
• C. $2^4$
• D. $6^4$

Answer 1

Answer: (B)

$2^8$

Answer 2

∣A∣=logx⋅logy⋅logz1​∣∣​logxlogxlogx​logy2logylogy​logzlogz3logz​∣∣​=2
⇒∣∣​adj(adjA2)∣∣​=∣∣​A2∣∣​4=28