Correct choice is (a) \(\frac{EI}{l^3}\begin{bmatrix}12&6l&-12&6l\\6l&4l^2&-6l&2l^2\\-12&-6l&12&-6l\\6l&2l^2&-6l&4l^2\end{bmatrix}\)

For explanation I would say: The value of stiffness matrix is given by

k=\(\frac{EI}{l^3}\begin{bmatrix}12&6l&-12&6l\\6l&4l^2&-6l&2l^2\\-12&-6l&12&-6l\\6l&2l^2&-6l&4l^2\end{bmatrix}\)

Here l is length of beam element, and E is the modulus of elasticity, and I moment of inertia of the beam element. The stiffness matrix of the beam element affects the displacement of the nodes and their interpolation in the beam element. The beam element stiffness matrix is a symmetric matrix.