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Prove that the Matrix 1 √ 3 [ 1 1 + I 1 1 − I − 1 ] is Unitary. - Applied Mathematics 1

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
  Is there an error in this question or solution?
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