If A =[(n,0,0)(0,n,0)(0,0,n)] and B = [(a1,a2,a3)(b1,b2,b3)(c1,c2,c3)],then AB is equal to :

Question

If A = \(\begin{bmatrix} n &0 & 0 \\[0.3em] 0 &n & 0 \\[0.3em] 0 & 0 & n \end{bmatrix}\) and B = \(\begin{bmatrix} a_1 &a_2 & a_3 \\[0.3em] b_1 &b_2 & c_3 \\[0.3em] c_1 & c_2 & c_3 \end{bmatrix}\), then AB is equal to :

A. B 

B. nB 

C. Bⁿ 

D. A + B

Answer 1

 (B). nB

AB = \(\begin{bmatrix} n &0 & 0 \\[0.3em] 0 &n & 0 \\[0.3em] 0 & 0 & n \end{bmatrix}\)x \(\begin{bmatrix} a_1 &a_2 & a_3 \\[0.3em] b_1 &b_2 & c_3 \\[0.3em] c_1 & c_2 & c_3 \end{bmatrix}\) 

Option (B) is the answer.