Let x, y, z > 1 and . The |adj (adj A2)| is equal to

Engineering

Mathematics

Introduction to Logarithm

Question

Let x, y, z > 1 and $A = [\begin{array}{ccc} 1 & \log_{x} y & \log_{x} z \\ \log_{y} x & 2 & \log_{y} z \\ \log_{z} x & \log_{z} y & 3 \end{array}]$ . The |adj (adj A²)| is equal to

2⁴

2⁸

6⁴

4⁸

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Let log x = t₁, log y = t₂, log z = t₃

$\Rightarrow | A | = |\begin{array}{ccc} 1 & \frac{t_{2}}{t_{1}} & \frac{t_{3}}{t_{1}} \\ \frac{t_{1}}{t_{2}} & 2 & \frac{t_{3}}{t_{2}} \\ \frac{t_{1}}{t_{3}} & \frac{t_{2}}{t_{3}} & 3 \end{array}| = 2$

Now, |Adj (Adj(A²))| = |Adj A²|² = (|A²|²)² = |A|⁸

= 2⁸

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