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If A=(2,0,0),(0,2,0),(0,0,2) Then A^6 - Mathematics and Statistics

MCQ

if  `A=[[2,0,0],[0,2,0],[0,0,2]]` then A6=  ......................

Options

  • 6A

  • 12A

  • 16A

  • 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,`

=26 x I,since I6=I

=2 5 x A [∵ A=2I]

=32A 

  Is there an error in this question or solution?
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