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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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