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Questions  >>  CBSE XII  >>  Math  >>  Determinants
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True or False: $\mid adj A\mid={\mid A\mid}^2$,where A is a square matrix of order two.

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A)
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  • If A is a non-singular matrix of order n then $|adj (A)|=|A|^{n-1}$
Given |adj A| where A is a square matrix of order two.
We know $|adj (A)|=|A|^{n-1}$
Here n=2.
Therefore $|adj (A)|=|A|^{2-1}$
$\qquad\qquad\qquad\;\;=|A|^1$
$\qquad\qquad\qquad\;\;=|A|$
Therefore $|adj (A)|=|A|$,when A is a square matrix of order two.
Hence |adj A|=$|A|^2$ is False.
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