A) \[4\]
B) \[5\]
C) \[6\]
D) \[7\]
Correct Answer: C
Solution :
[c] As given: \[\left| {{A}_{n\times n}} \right|=3\] and \[\left| adj\,\,A \right|=243\] Determinant of adjoint A 13 given by: \[\left| adj\,\,A \right|={{\left| {{A}_{n\times n}} \right|}^{n-1}}\] \[\Rightarrow 243={{3}^{n-1}}\Rightarrow {{3}^{5}}={{3}^{n-1}}\Rightarrow n-1=5\] \[\Rightarrow n=6\]
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