Question

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

विकल्प

• 6A

• 12A

• 16A

• 32A

Answer 1

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