Select and write the most appropriate answer from the given alternatives in each of the following :
If `A = {:((2,0,0),(0,2,0),(0,0,2)):}," then " A^(6) = ` .........

Options

A. 6A
B. 12A
C. 16A
D. 32A

Answer

D

Explanation

`A = [(2,0,0),(0,2,0),(0,0,2)] = 2 [(1,0,0),(0,1,0),(0,0,1)] = 2 I`
`A^(6) = (2I)^(6)` ltbr ` = (2)^(5) xx 2 (I)^(6)`
` = (2)^(5) xx 2I" "[:' I^(6) = I]`
` = 2^(5) xx A" "[:' 2I = A]`
` = 32 A`
Hence, the correct answer from the given alternative is (d).