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Question
if `A=[[2,0,0],[0,2,0],[0,0,2]]` then A6= ......................
Options
6A
12A
16A
32A
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,`
=26 x I,since I6=I
=2 5 x A [∵ A=2I]
=32A
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