#### Please Solve R.D.Sharma class 12 Chapter 4 Algbra of Matrices Exercise Multiple Choice Questions Question 10 Maths textbook Solution.

Answer: The correct option is (B), AB = nB

Given:$A=\left[\begin{array}{lll} n & 0 & 0 \\ 0 & n & 0 \\ 0 & 0 & n \end{array}\right] \text { and } B=\left[\begin{array}{lll} a_{1} & a_{2} & a_{3} \\ b_{1} & b_{2} & b_{3} \\ c_{1} & c_{2} & c_{3} \end{array}\right]$

Solution:\begin{aligned} A B &=\left[\begin{array}{lll} n & 0 & 0 \\ 0 & n & 0 \\ 0 & 0 & n \end{array}\right] \times\left[\begin{array}{lll} a_{1} & a_{2} & a_{3} \\ b_{1} & b_{2} & b_{3} \\ c_{1} & c_{2} & c_{3} \end{array}\right] \\ &=\left[\begin{array}{lll} n a_{1}+0+0 & n a_{2}+0+0 & n a_{3}+0+0 \\ 0+n b_{1}+0 & 0+n b_{2}+0 & 0+n b_{3}+0 \\ 0+0+n c_{1} & 0+0+n c_{2} & 0+0+n c_{3} \end{array}\right] \\ &=\left[\begin{array}{lll} n a_{1} & n a_{2} & n a_{3} \\ n b_{1} & n b_{2} & n b_{3} \\ n c_{1} & n c_{2} & n c_{3} \end{array}\right] \end{aligned}

Now              \begin{aligned} &=n\left[\begin{array}{lll} a_{1} & a_{2} & a_{3} \\ b_{1} & b_{2} & b_{3} \\ c_{1} & c_{2} & c_{3} \end{array}\right] \\ &=\mathrm{nB} \end{aligned}

So, the option (B) is correct.