Question

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

• A. $3B$
• B. $\frac{1}{3}B$
• C. $3B^{-1}$
• D. $\frac{1}{3}{B}^{-1}$

Answer 1

The correct option is B

$\frac{1}{3}B$

$AB=3I$
Multiplying both the sides by $A^{-1},$ we get
$A^{-1}A\cdot B=3A^{-1}\cdot I$
$\Rightarrow I\cdot B=3A^{-1}$
$\Rightarrow A^{-1}=\frac{1}{3}B$