Need RD Sharma solution for Maths Class 12 Chapter 5 Determinants Exercise Very short question Question 6 for maths textbook solution.

Hint: Here we use basic concept and properties of determinant of  matrix

Given: $\left|\begin{array}{lll} 101 & 102 & 103 \\ 104 & 105 & 106 \\ 107 & 108 & 109 \end{array}\right|$

Solution :

Let's perform some row operations

\begin{aligned} &\mathrm{R}_{1} \rightarrow R_{1}-R_{2} \text { and } \mathrm{R}_{2} \rightarrow R_{2}-R_{3} \\ &\left|\begin{array}{ccc} -3 & -3 & -3 \\ -3 & -3 & -3 \\ 107 & 108 & 109 \end{array}\right| \end{aligned}

$\rightarrow$ Here we clearly see that 2 row's have same value

So, determinant of matrix must be zero

$\rightarrow$ Because according to property of determinate if 2 or more rows has same value then determinate's value is zero