State True or False for the statements

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.


True

Let A be the determinant.


|A| = 12


We know that if A is a square matrix of order n, then |adj A| = |A|n-1


For n = 3, |adj A| = |A|3-1


= |A|2


= 122 = 144


Hence the above statement is true.


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