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if A is an invertible matrix of order 3 and |A|=5, then find |adj.A|.

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  • $|adj A|=|A|^{n-1}$
Given:|A|=5 and order n=3.
 
We know |adj A|=$|A|^{n-1}$
 
Here n=3.
 
$|adj A|=|A|^{3-1}$
 
$\qquad\;=|A|^2$
 
Therefore $|adj\; A|=5^2$
 
$\qquad\qquad\qquad=25.$
 
Hence |adj A|=25.

 

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