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प्रश्न
If A is a singular matrix, then adj A is ______.
विकल्प
non-singular
singular
symmetric
not defined
उत्तर
If A is a singular matrix, then adj A is singular.
\[\text{ A is singular, so } \left| A \right| = 0\].
By definition, we have
A \[adj \left( A \right) = O \]
\[ \Rightarrow \left| A adj \left( A \right) \right| = \left| O \right|\]
\[ \Rightarrow \left| A \right| \left| adj \left( A \right) \right| = 0 \]
\[ \Rightarrow \left| adj \left( A \right) \right| = 0 \]
\[\text{ Hence, }adj \left( A \right)\text{ is singular}\].
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