Question
Mathematics Question on Algebra of Complex Numbers
If A is a square matrix of order 3, then |Adj(Adj A2)| =
A
|A|2
B
|A|4
C
|A|8
D
|A|16
Answer
|A|8
Explanation
Solution
The correct option is: (C): |A|8
The absolute value of the adjugate of matrix A, denoted as adjA, is equal to the absolute value of matrix A raised to the power of (n-1), where n represents the order of the determinant. This relationship leads to the conclusion that the absolute value of the adjugate of the adjugate of matrix A raised to the power of 2 is equal to the absolute value of matrix A raised to the power of 4, which, in turn, is equal to the absolute value of matrix A raised to the power of 8.
In mathematical terms: ∣adj(adj 2)∣=∣A2∣(3−1)2=∣A4∣=∣A∣8.∣adj(adjA2)∣=∣A2∣(3−1)2=∣A4∣=∣A∣8.