If A is a singular matrix, then adj A is ______.

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If A is a singular matrix, then adj A is singular. 	ext{ A is singular, so } \left| A ight| = 0. By definition, we have A adj \left( A ight) = O \Rightarrow \left| A adj \left( A ight) ight| = \left| O ight| \Rightarrow \left| A ight| \left| adj \left( A ight) ight| = 0 \Rightarrow \left| adj \left( A ight) ight| = 0 	ext{ Hence, }adj \left( A ight)	ext{ is singular}.

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