#### Need Solution for  R.D.Sharma Maths Class 12 Chapter determinants  Exercise 5.2 Question 46 Maths Textbook Solution.

Hint Use determinant formula

Given: $\left|\begin{array}{lll} a & b & c \\ x & y & z \\ p & q & r \end{array}\right|=\left|\begin{array}{lll} x & y & z \\ p & q & r \\ a & b & c \end{array}\right|=\left|\begin{array}{lll} y & b & q \\ x & a & p \\ z & c & r \end{array}\right|$

Solution:

\begin{aligned} &\left|\begin{array}{lll} a & b & c \\ x & y & z \\ p & q & r \end{array}\right|=\left|\begin{array}{lll} x & y & z \\ p & q & r \\ a & b & c \end{array}\right| \\ &R_{1} \leftrightarrow R_{3}, R_{2} \leftrightarrow R_{1}, R_{3} \leftrightarrow R_{1} \\ &=(-)(-)\left|\begin{array}{lll} x & y & z \\ a & b & c \\ p & q & r \end{array}\right| \end{aligned}

For interchanging R2↔R3

Now convert rows in columns and column in row
\begin{aligned} &\left|\begin{array}{lll} x & y & z \\ p & q & r \\ a & b & c \end{array}\right|=\left|\begin{array}{lll} x & p & a \\ y & q & b \\ z & r & c \end{array}\right| \\ &\text { Now } R_{1} \leftrightarrow R_{2}, C_{2} \leftrightarrow C_{3} \\ &(-)(-)\left|\begin{array}{lll} y & q & b \\ x & p & a \\ z & r & c \end{array}\right|=\left|\begin{array}{lll} y & b & q \\ x & a & p \\ z & c & r \end{array}\right| \end{aligned}