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Question: If A = \(\begin{bmatrix} i & 0 \\ 0 & i \end{bmatrix}\), n Ī N, then A<sup>4n</sup> equals –...

If A = [i00i]\begin{bmatrix} i & 0 \\ 0 & i \end{bmatrix}, n Ī N, then A4n equals –

A

[1001]\begin{bmatrix} 1 & 0 \\ 0 & 1 \end{bmatrix}

B

[i00i]\begin{bmatrix} i & 0 \\ 0 & i \end{bmatrix}

C

[0ii0]\begin{bmatrix} 0 & i \\ i & 0 \end{bmatrix}

D

[0000]\begin{bmatrix} 0 & 0 \\ 0 & 0 \end{bmatrix}

Answer

[1001]\begin{bmatrix} 1 & 0 \\ 0 & 1 \end{bmatrix}

Explanation

Solution

A2=[–100–1]\begin{bmatrix} –1 & 0 \\ 0 & –1 \end{bmatrix}ŽA4=[1001]\begin{bmatrix} 1 & 0 \\ 0 & 1 \end{bmatrix}=IŽA4n=(I)n=I`