Question

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

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

Answer 1

Answer: (B)

$\frac{1}{3}B$

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