Prove that the matrix `1/sqrt3` `[[ 1,1+i1],[1-i,-1]]` is unitary.
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Solution
Let A= `1/sqrt3[[ 1,1+i],[1-i,-1]]`
The matrix is unitary when A.𝑨𝜽 = 𝑰 .
∴ `A^θ=(\bar{A})^t=1/sqrt3[[ 1,1+i],[1-i,-1]]^t =1/sqrt3[[ 1,1+i],[1-i,-1]]`
∴ `A.A^θ=1/sqrt3[[ 1,1+i],[1-i,-1]]1/sqrt3[[ 1,1+i],[1-i,-1]]`
= `1/3 [[3,0],[0,3]]`
=`[[1,0],[0,1]]`
∴` A.A^θ=I`
The given matrix is unitary is proved.
Concept: .Circular Functions of Complex Number
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