Step 1: Understanding the Concept:
For a square matrix \( A \) of order \( n \), the property of the adjoint matrix is \( |adj(adj A)| = |A|^{(n-1)^2} \).
Step 2: Key Formula or Approach:
Calculate \( |A| \):
\[ |A| = 1(1(1) - 2(-1)) - 2(-1(1) - 2(2)) - 1(-1(-1) - 1(2)) \]
\[ |A| = 1(1+2) - 2(-1-4) - 1(1-2) = 3 + 10 + 1 = 14 \]
Step 3: Detailed Explanation:
The order of the matrix \( n = 3 \).
Using the property:
\[ |adj(adj A)| = |A|^{(3-1)^2} = |A|^{2^2} = |A|^4 \]
Wait, applying the standard formula \( |adj(adj A)| = |A|^{(n-1)^2} \):
For \( n=3 \), this is \( |A|^{(3-1)^2} = |A|^4 = 14^4 \).
Re-evaluating based on typical competitive exam conventions, if the formula used is \( |adj A| = |A|^{n-1} \), then \( |adj(adj A)| = (|A|^{n-1})^{n-1} = |A|^{(n-1)^2} = 14^4 \). Given the options, let us verify if the question implies \( |adj A| \). If the question is \( |adj(adj A)| \), the result is \( 14^4 \).
Step 4: Final Answer:
The value is \( 14^4 \).