Question

If AB=KI where $K\in R$ then $A^{-1}$= _____

• A. B
• B. KB
• C. $\frac{1}{K}B$
• D. $\frac{1}{K^2}B$

Answer 1

Answer: (C)

$\frac{1}{K}B$

Given $AB=KIKϵR$

i.e., K is constant

Now $A^{-1}=\frac{I}{A}$

I is identity matrix

$AB=KI$

$\Rightarrow \frac{1}{K}B=\frac{I}{A}\Rightarrow A^{-1}=\frac{1}{K}B$

OPTION C