I am trying to implement the HHL algorithm (for solving $Ax=b$). I am assuming $A$ to be unitary and Hermitian so that I can find the Hamiltonian simulation for it easily. 
For any $A$ to be Hermitian and unitary, it has to be of form,
$$ A = \begin{pmatrix} x & \pm\sqrt{1-x^2}\\ \pm\sqrt{1-x^2} & x\end{pmatrix} $$
I reduced $e^{i\alpha A}$ to following (by using formula $e^{i\theta A} = (\cos\theta)I + i(\sin\theta)A$ where $A^2=I$), but I don't know how to implement it on Qiskit.
$$ e^{i\alpha A} = \begin{pmatrix} \cos\alpha+i\sin\alpha\cos\frac{\theta}{2} & i\sin\alpha \sin\frac{\theta}{2} \\ i\sin\alpha \sin\frac{\theta}{2} & \cos\alpha+i\sin\alpha\cos\frac{\theta}{2} \end{pmatrix} .$$
where $\theta = 2\cos^{-1}{x}$. How to construct this gate?