### Matrices Question 4

#### Question 4 - 25 January - Shift 1

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

(1) $6^{4}$

(2) $2^{8}$

(3) $4^{8}$

(4) $2^{4}$

## Show Answer

#### Answer: (2)

#### Solution:

#### Formula: Properties of Adjoint of a Matrix, Properties of Matrix Multiplication

$|A|=\frac{1}{\log x \cdot \log y \cdot \log z} \begin{vmatrix} \log x & \log y & \log z \\ \log x & 2 \log y & \log z \\ \log x & \log y & 3 \log z\end{vmatrix} =2$

$\Rightarrow|adj(adj A^{2})|=|A^{2}|^{4}=2^{8}$