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What product? The product of the two matrices in post #5 is ##\begin{pmatrix}i & 0 \\ 0 & i\end{pmatrix}##. As HallsofIvy said, the inverse of ##\begin{pmatrix}1 & 0\\ 0 & i\end{pmatrix}## is ##\begin{pmatrix}1 & 0\\ 0 & -i\end{pmatrix}##. The product of these two matrices is the identity matrix.Right the product will result in the inverse:
1 0
0 1
correct ?