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Questions  >>  JEEMAIN and NEET  >>  Mathematics  >>  Class12  >>  Determinants
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Q)

If A is singular matrix then adj.A is

$\begin{array}{1 1}(A)\;\text{Singular}&(B)\;\text{Non-singular}\\(C)\;\text{Symmetric}&(D)\;\text{Not defined}\end{array}$

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A)
As $A.adj.A=|A|.I$[A is of order $n\times n]$
$\mid A.adj.A\mid=\mid A\mid^n$
$\mid A\mid.\mid adj.A\mid=\mid A\mid^n$
As A is singular
$\mid A\mid=0$
$\Rightarrow \mid adj.A\mid=0$
$\therefore adj \;A$ is singular.
Hence (A) is the correct answer.
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