if `A[{:(5,-3),(111,336):}]` and det`(-3A^(2013)+A^(2014))=alpha^(alpha)+beta^(2)(1+gamma+gamma^(2))` where `alpha,beta,gamma` are natural numbers and `(alphagtgammagtbeta)` then

Options

A. `alpha+beta=2016`
B. `alpha+beta=2023`
C. `alpha+beta+gamma=2026`
D. `beta+gamma=13`

Answer

A, C, D

Explanation

`because-3A^(2013)+A^(2014)=A^(2013)(A-3I)`
`becausedet(-3A^(2013)+A^(2014))=|A^(2012)(A-3I)|`
`=|A|^(2013)|A-3I|=(2013)^(2013)(999)`
`(2013)^(2013)3^(2)(1+10+10^(2))`