Question

There are at least three unitary matrices of order 2. True or false with full explanation

Answer 1

Answer:

By definition a matrix U is defined as unitary if

UU^θ = U^θU=1

Where U^θ is conjugate transpose of U.

Now take A= $\begin{bmatrix} 1 & 0 \\ 0 & 1 \end{bmatrix}$ , then A^θ =A and A^θ A=AA^θ =1

Take take A=  $\begin{bmatrix} 1 & 0 \\ 0 & -1 \end{bmatrix}$ , then A^θ =A and A^θ A=AA^θ =1

take A=$\begin{bmatrix} -1 & 0 \\ 0 & 1 \end{bmatrix}$ , then A^θ =A and A^θ A=AA^θ =1

It can be concluded that at least three unitary 2 x 2 matrices. Hence it is true.