If and , then AB is equal to

Engineering

Mathematics

Multiplication of Matrices

Question

If $A = [\begin{array}{ccc} n & 0 & 0 \\ 0 & n & 0 \\ 0 & 0 & n \end{array}]$ and $B = [\begin{array}{ccc} a_{1} & a_{2} & a_{3} \\ b_{1} & b_{2} & b_{3} \\ c_{1} & c_{2} & c_{3} \end{array}]$ , then AB is equal to

Bⁿ

A + B

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Let, $A = [\begin{array}{ccc} n & 0 & 0 \\ 0 & n & 0 \\ 0 & 0 & n \end{array}]$ and

B = [\begin{array}{ccc} a_{1} & a_{2} & a_{3} \\ b_{1} & b_{2} & b_{3} \\ c_{1} & c_{2} & c_{3} \end{array}]

Now,

AB = [\begin{array}{ccc} n & 0 & 0 \\ 0 & n & 0 \\ 0 & 0 & n \end{array}] [\begin{array}{ccc} a_{1} & a_{2} & a_{3} \\ b_{1} & b_{2} & b_{3} \\ c_{1} & c_{2} & c_{3} \end{array}]

AB = [\begin{array}{ccc} {na}_{1} & {na}_{2} & {na}_{3} \\ {nb}_{1} & {nb}_{2} & {nb}_{3} \\ {nc}_{1} & {nc}_{2} & {nc}_{3} \end{array}]

or, AB = nB.

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