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Question
If the value of a third order determinant is 12, then the value of the determinant formed by replacing each element by its co-factor will be 144.
Options
True
False
Solution
This statement is True.
Explanation:
Since |A| = 12
If A is a square matrix of order n
Then |Adj A| = `|"A"|^("n" - 1)`
∴ |Adj A| = `|"A"|^(3 - 1)`
= |A|2
= (12)2
= 144 ...[n = 3]
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