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Let A=[(a,0, 0),( 0,a,0),( 0, 0,a)] , t...

Let `A=[(a,0, 0),( 0,a,0),( 0, 0,a)]` , then `A^n` is equal to `[(a^n,0, 0),( 0,a^n,0),(0, 0,a)]` (b) `[(a^n,0 ,0),( 0,a,0 ),(0, 0,a)]` (c) `[(a^n,0, 0),( 0,a^n,0),( 0, 0,a^n)]` (d) `[(n a,0, 0),( 0,n a,0 ),(0, 0,n a)]`

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Given: `A=[(a,0, 0),( 0,a,0),( 0, 0,a)]`
Then
`A^2=[(a,0, 0),( 0,a,0),( 0, 0,a)] [(a,0, 0),( 0,a,0),( 0, 0,a)]`
`A^2=[(a^2,0, 0),( 0,a^2,0),( 0, 0,a^2)]`
Now
`A^3=A^2.A=[(a^2,0, 0),( 0,a^2,0),( 0, 0,a^2)][(a,0, 0),( 0,a,0),( 0, 0,a)]`
`A^3=[(a^3,0, 0),( 0,a^3,0),( 0, 0,a^3)]`
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