A) \[{{(\left| A \right|+K)}^{n-2}}\]
B) \[{{(\left| A \right|+K)}^{n}}\]
C) \[{{(\left| A \right|+K)}^{n-1}}\]
D) none of these
Correct Answer: B
Solution :
[b] We have, AB = A(adj A)\[=\left| A \right|{{I}_{n}}\] \[\therefore AB+K{{I}_{n}}=\left| A \right|{{I}_{n}}+K{{I}_{n}}=(\left| A \right|+k){{I}_{n}}\] \[\Rightarrow \left| AB+K{{I}_{n}} \right|=\left| (\left| A \right|+K){{I}_{n}} \right|\] (\[\therefore \left| \alpha {{I}_{n}} \right|={{\alpha }^{n}}\]) \[={{(\left| A \right|+K)}^{n}}\]
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