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Maths-

General

Easy

Question

If A = $open square brackets table row i 0 row 0 i end table close square brackets$ , n $element of$ N, then A⁴ⁿ equals -

$[\begin{matrix} 1 & 0 \\ 0 & 1 \end{matrix}]$
$[\begin{matrix} i & 0 \\ 0 & i \end{matrix}]$
$[\begin{matrix} 0 & i \\ i & 0 \end{matrix}]$
$[\begin{matrix} 0 & 0 \\ 0 & 0 \end{matrix}]$

The correct answer is: $open square brackets table row 1 0 row 0 1 end table close square brackets$

A²= $open square brackets table row cell – 1 end cell 0 row 0 cell – 1 end cell end table close square brackets$ $rightwards double arrow$ A⁴= $open square brackets table row 1 0 row 0 1 end table close square brackets$ =I $rightwards double arrow$ A⁴ⁿ=(I)ⁿ=I

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