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

$(a)\;3B\qquad(b)\;\large\frac{1}{3}$$B\qquad(c)\;3B^{-1}\qquad(d)\;\large\frac{1}{3}$$B^{-1}$

Given
$AB=3I$
Multiply $A^{-1}$ on both the side
$A^{-1}(AB)=A^{-1}(3I)$
$B=3A^{-1}$
$A^{-1}=\large\frac{B}{3}$
Hence (b) is the correct answer.
edited Mar 19, 2014