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Question
The value of the determinant of a matrix A of order 3 is 3. If C is the matrix of cofactors of the matrix A, then what is the value of determinant of C2?
Solution
n = 3
|A| = 3.
As per question,
C = (adj A)T
∴ |C| = |(adj A)T|
= |adj A|
∴ |C| = |A|n – 1
= 33 – 1
= 32
= 9
|C2| = |C| · |C|
= 9 × 9
= 81
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