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if A=[[i,0] , [0,i]] where i=sqrt(-1) an...

if `A=[[i,0] , [0,i]]` where `i=sqrt(-1)` and `x epsilon N` then `A^(4x)` equals to:

Text Solution

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`A^(2)=[(i,0),(0,i)][(i,0),(0,i)]=[(i^(2),0),(0,i^(2))]=[(-1,0),(0,-1)]`
`A^(4)=[(-1,0),(0,-1)][(-1,0),(0,-1)]=[(1,0),(0,1)]=I`
`implies A^(4n)=I^(n)=I`
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