then the inverse of A/2 will be
A) 2A
B) \[\frac{{{A}^{-1}}}{2}\]
C) \[\frac{A}{2}\]
D) \[{{A}^{2}}\]
Correct Answer: A
Solution :
[a] A is involuntary. Hence, \[{{A}^{2}}=I\Rightarrow A={{A}^{-1}}\] Also, \[{{(kA)}^{-1}}=\frac{1}{k}{{(A)}^{-1}}\] Or \[{{\left( \frac{1}{2}A \right)}^{-1}}=2{{(A)}^{-1}}\]or 2A
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