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True or False: 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.

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1 Answer

Toolbox:
  • $|adj (A)|=|A|^{n-1}$
Given: The value of a third order determinant is 12.
The determinant formed by replacing each element by its cofactor is |adj A|.
From the information in the toolbox we know,
$|adj (A)|=|A|^{n-1}$
Since it is a 3 order determinant n=3.
Therefore $|adj (A)|=|A|^2$
But |A|=12.
$|adj (A)|=12^2=144$
Hence True.
answered Mar 27, 2013 by sreemathi.v
 

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