explain solution RD Sharma class 12 chapter 5 Determinants exercise Fill in the blanks question 4 maths

Answer: $K^{2}$

Hint: Here, we use basic concept of singular matrix

Given: A and B non singular square matrix of order ‘n’

Such that A = KB

Solution: Here, A and B are non singular

And both are n order of singular matrix

Here

$A=KB$

$\left | A \right |=\left | K \right |\left | B \right |$            (Let's take both side determinate)

$\left | A \right |=K^{n}\left | B \right |$

$\frac{\left | A \right |}{\left |B \right |}=K^{n}$                    [A and B are $n\times n$ matrix]

So,           $\frac{\left | A \right |}{\left |B \right |}=K^{n}$