Let i = 1 and let A = [ i 0 0 i ] and B = [ 0 i i 0]. (a) Find A2, A3, and A4. Identify

Chapter 8, Problem 109

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Exploration Let \(i=\sqrt{-1}\) and let

\(A=\left[\begin{array}{cc} i & 0 \\ 0 & i \end{array}\right]\) and \(B=\left[\begin{array}{rr} 0 & -i \\ i & 0 \end{array}\right]\)

(a) Find \(A^2,\ A^3\) and \(A^4\). Identify any similarities with \(i^2,\ i^3,\) and \(i^{4}\).

(b) Find and identify \(B^{2}\).

Text Transcription:

i = sqrt -1

A = [ _0  i  ^i  0]

B = [ _i  0  ^0  -i]

A^2, A^3

A^4

i^2, i^3

i^4

B^2