More details would help, but in general I'd expect a full traceability matrix to include columns for design elements which could be split between high level and low level design.
I should be able to trace a specific business requirement to a technical/system requirement and that in turn to a high-level design element/component and that in turn to a low-level one.
How you identify those design components is driven by your organization standards - usually some sort of unique ID would be used referencing back to content within a design document.
