With the advent of Large Language Models (LLMs) and Multimodal (Visio-lingual) LLMs, a flurry of research has emerged, analyzing the performance of such models across a diverse array of tasks. While most studies focus on evaluating the capabilities of state-of-the-art (SoTA) MLLM models through task accuracy (e.g., Visual Question Answering, grounding) across various datasets, our work explores the related but complementary aspect of consistency - the ability of an MLLM model to produce semantically similar or identical responses to semantically similar queries. We note that consistency is a fundamental prerequisite (necessary but not sufficient condition) for robustness and trust in MLLMs. Humans, in particular, are known to be highly consistent (even if not always accurate) in their responses, and consistency is inherently expected from AI systems. Armed with this perspective, we propose the MM-R$^3$ benchmark, which analyses the performance in terms of consistency and accuracy in SoTA MLLMs with three tasks: Question Rephrasing, Image Restyling, and Context Reasoning. Our analysis reveals that consistency does not always align with accuracy, indicating that models with higher accuracy are not necessarily more consistent, and vice versa. Furthermore, we propose a simple yet effective mitigation strategy in the form of an adapter module trained to minimize inconsistency across prompts. With our proposed strategy, we are able to achieve absolute improvements of 5.7% and 12.5%, on average on widely used MLLMs such as BLIP-2 and LLaVa 1.5M in terms of consistency over their existing counterparts.