Fine-tuning pre-trained large language models (LLMs) on a diverse array of tasks has become a common approach for building models that can solve various natural language processing (NLP) tasks. However, where and to what extent these models retain task-specific knowledge remains largely unexplored. This study investigates the task-specific information encoded in pre-trained LLMs and the effects of instruction tuning on their representations across a diverse set of over 60 NLP tasks. We use a set of matrix analysis tools to examine the differences between the way pre-trained and instruction-tuned LLMs store task-specific information. Our findings reveal that while some tasks are already encoded within the pre-trained LLMs, others greatly benefit from instruction tuning. Additionally, we pinpointed the layers in which the model transitions from high-level general representations to more task-oriented representations. This finding extends our understanding of the governing mechanisms of LLMs and facilitates future research in the fields of parameter-efficient transfer learning and multi-task learning.