#### Provide Solution For  R.D.Sharma Maths Class 12 Chapter 4 Algebra of Matrices Exercise Multiple Choice Questions  Question 15 Maths Textbook Solution.

Answer: The correct option is (C).

Given:$S=\left[S_{i j}\right] \text { and } S_{\ddot{j}}=\mathrm{K}$

Solution: \begin{aligned} &S=\left[S_{i j}\right] \\ &S=\left[\begin{array}{cc} K & 0 \\ 0 & K \end{array}\right] \quad\left(\mathrm{As}_{3} S_{i j}=\mathrm{K}\right) \end{aligned}

$\text { Let } A=\left[\begin{array}{ll} a_{11} & a_{12} \\ a_{21} & a_{22} \end{array}\right]$                                                                              (Square Matrix)

\begin{aligned} A S &=\left[\begin{array}{ll} a_{11} & a_{12} \\ a_{21} & a_{22} \end{array}\right] \times\left[\begin{array}{cc} K & 0 \\ 0 & K \end{array}\right] \\ &=\left[\begin{array}{ll} K a_{11} & K a_{12} \\ K a_{21} & K a_{22} \end{array}\right] \\ &=K\left[\begin{array}{ll} a_{11} & a_{12} \\ a_{21} & a_{22} \end{array}\right] \\ &=K A \end{aligned}

Hence,

$A S=S A=K A$

So, the correct option is (C).