Can the transformation matrix of a 3-D beam element have any zeros in its diagonal?

Hello,

I am trying to solve the global stiffness matrix for a component assumed to be a series of 3-D beam elements.

Some of the diagonal elements of the transformation matrix are zeros and i eventually end up in finding the inverse of a matrix with some zeros in  its diagonal which is not possible.

Can anyone let me know if the transformation matrix can have zeros along its diagonal?

Thank you.