#### Please Solve RD Sharma Class 12 Chapter Algebra of Matrices Exercise 4.1 Question 5 Suquestion (ii) Maths Textbook Solution.

Answer: $A= \begin{bmatrix} 0 &\frac{1}{2} \\ \frac{1}{2} & 0 \end{bmatrix}$

Given: $\frac{\left ( i-j \right )^{2}}{2}$
Here we have to construct $2\times 2$  matrix according to $\frac{\left ( i-j \right )^{2}}{2}$

Hint:     Substitute required values in the $2\times 2$  matrix

Solution:  Let $A= \left [ a_{ij} \right ]_{2\times 2}$

So, the elements in a $2\times 2$  are $a_{11},a_{12},a_{21},a_{22}$

$A= \begin{bmatrix} a_{11} &a_{12} \\ a_{21} & a_{22} \end{bmatrix}$

$\! \! \! \! \! \! \! \! \! a_{11}= \frac{\left ( 1-1 \right )^{2}}{2}= 0\\a_{12}= \frac{\left ( 1-2 \right )^{2}}{2}= \frac{\left ( 1 \right )^{2}}{2}= \frac{1}{2}$                              $\! \! \! \! \! \! \! \! \! a_{21}= \frac{\left ( 2-1 \right )^{2}}{2}=\frac{1 }{2}\\a_{22}= \frac{\left ( 2-2 \right )^{2}}{2}=0$

Substituting these values in Matrix $A$ , we get

$A= \begin{bmatrix} 0 &\frac{1}{2} \\ \frac{1}{2} & 0 \end{bmatrix}$