Question

If A is an invertible matrix of order n and k is any positive real number, then the value of $\left[det\right(kA){]}^{-1}detA$ is

• A. $k^{-n}$
• B. $k^{-1}$
• C. $k^n$
• D. $nk$

Answer 1

Answer: (A)

$k^{-n}$

To find: $\left[det\right(kA){]}^{-1}detA=?$

We know that if $A$ is invertible matrix of order n, then

$\left[det\right(kA\left)\right]=k^{n}detA$

Now,

$\left[det\right(kA){]}^{-1}detA=\frac{1}{k^{n}detA}\times detA=k^{-n}$

Hence, A is the correct option.