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  4. If A and B are square matrices of the same order and AB = 3I, then A-1 is equal to

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Q. If $A$ and $B$ are square matrices of the same order and $AB = 3I$, then $A^{-1}$ is equal to

WBJEEWBJEE 2009Matrices

Solution:

Since, $AB=3I$
$\Rightarrow A^{-1}AB=3IA^{-1}$
$\Rightarrow B=3A^{-1}$
$\Rightarrow A^{-1}=\frac{B}{3}$