#### Question

^{if `A=[[2,0,0],[0,2,0],[0,0,2]]`} then A^{6}=^{ ......................}

(a) 6A

(b) 12A

(c) 16A

(d) 32A

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#### Solution

i. **(d)**

Given that

`A=[[2,0,0],[0,2,0],[0,0,2]]`

we can write

`A=2[[1,0,0],[0,1,0],[0,0,1]]`

Here 2 is scalar multiple

Terefore ,A=2 x I, where I= `[[1,0,0],[0,1,0],[0,0,1]]`

thus ,`A^6={2[[1,0,0],[0,1,0],[0,0,1]]}^6`

` =2^6xx[[1,0,0],[0,1,0],[0,0,1]]^6`

`=2^6xxI^6,`

=**2 ^{6} x I,since I^{6}=I**

**=2 ^{ 5 }x A [**∵

**A=2I]**

**=32A**

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Solution for question: if A=[[2,0,0],[0,2,0],[0,0,2]] then A^6 concept: Operations on Matrices - Addition of Matrices. For the courses HSC Arts, HSC Science (Computer Science), HSC Science (Electronics), HSC Science (General)