Describe how you would handle the computational challenges and data sparsity in your matrix multiplication using a suitable pseudoinverse. Explain the tradeoffs involved.

I would use the Moore-Penrose Pseudoinverse to stabilize the computation of the user-item interaction matrix. This approach provides a numerically stable solution even when dealing with sparse or underdetermined matrices, at the cost of introducing some bias in the recommendation results due to the pseudoinverse’s optimization criteria.