Question

if A is a square matrix of order n and A=kB where k is a scalar then IAI=

a. IBI
b. KIBI
c. K^nIBI
d. nIBI​

Answer 1

Answer:

K^ n|B| is the correct answer

Answer 2

Given,

A is a square matrix of order n.

$\[A = kB\]$, where k is a scalar.

Solution,

It is given that square matrix has order of n. So it has n rows and n column.

$\[A = kB\]$

To satisfy the above condition both matrix should have same order.

k is the scalar that is taken common from each row. There are n rows so k will be $\[{k^n}\]$.

So the determinant will be,

$\[|A| = {k^n}|B|\]$

Hence the correct option is (c), i.e. $\[|A| = {k^n}|B|\]$