Despite the growing interest in Mamba architecture as a potential replacement for Transformer architecture, parameter-efficient fine-tuning (PEFT) approaches for Mamba remain largely unexplored. In our study, we introduce two key insights-driven strategies for PEFT in Mamba architecture: (1) While state-space models (SSMs) have been regarded as the cornerstone of Mamba architecture, then expected to play a primary role in transfer learning, our findings reveal that Projectors---not SSMs---are the predominant contributors to transfer learning, and (2) Based on our observation that adapting pretrained Projectors to new tasks can be effectively approximated through a near-diagonal linear transformation, we propose a novel PEFT method specialized to Mamba architecture: Projector-targeted Diagonal-centric Linear Transformation (ProDiaL). ProDiaL focuses on optimizing only diagonal-centric linear transformation matrices, without directly fine-tuning the pretrained Projector weights. This targeted approach allows efficient task adaptation, utilizing less than 1% of the total parameters, and exhibits strong performance across both vision and language Mamba models, highlighting its versatility and effectiveness.