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Maths-

General

Easy

Question

If A = $open square brackets table row 3 cell negative 4 end cell row 1 cell negative 1 end cell end table close square brackets$ , then for every positive integer n, Aⁿ is equal to -

$[\begin{matrix} 1 + 2 n & 4 n \\ n & 1 + 2 n \end{matrix}]$
$[\begin{matrix} 1 + 2 n & - 4 n \\ n & 1 - 2 n \end{matrix}]$
$[\begin{matrix} 1 - 2 n & 4 n \\ n & 1 + 2 n \end{matrix}]$
None of these

The correct answer is: $open square brackets table row cell 1 plus 2 n end cell cell negative 4 n end cell row n cell 1 minus 2 n end cell end table close square brackets$

we are given A and need to find $A to the power of n$
$A equals open square brackets table row 3 cell negative 4 end cell row 1 cell negative 1 end cell end table close square brackets therefore A squared equals open square brackets table row 3 cell negative 4 end cell row 1 cell negative 1 end cell end table close square brackets open square brackets table row 3 cell negative 4 end cell row 1 cell negative 1 end cell end table close square brackets space equals open square brackets table row 5 8 row 2 5 end table close square brackets therefore A cubed equals open square brackets table row 5 8 row 2 5 end table close square brackets open square brackets table row 3 cell negative 4 end cell row 1 cell negative 1 end cell end table close square brackets space therefore A cubed space equals open square brackets table row 7 12 row 3 7 end table close square brackets therefore A to the power of 4 equals open square brackets table row 7 12 row 3 7 end table close square brackets open square brackets table row 3 cell negative 4 end cell row 1 cell negative 1 end cell end table close square brackets therefore A to the power of 4 space equals open square brackets table row 9 16 row 4 9 end table close square brackets therefore A to the power of n space space equals open square brackets table row cell 1 plus 2 n end cell cell 4 n end cell row cell space n end cell cell space space space space space space space space 1 plus 2 n space space end cell end table close square brackets$

Therefore the correct option is choice 2

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