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The current computing era enables the generation of vast amounts of data, which must be processed to extract valuable insights. This processing often requires multiple query operations, where hashing plays a crucial role in accelerating query response times. Among hashing techniques, Cuckoo Hashing has demonstrated greater efficiency than conventional methods, offering simplicity and ease of integration into various real-world applications. However, Cuckoo Hashing also has limitations, including data collisions, data loss due to collisions, and the potential for endless loops that lead to high insertion latency and frequent rehashing. To address these challenges, this work introduces a modified Matrix hashing technique. The core concept of the proposed scheme is to utilize both a 2D array and an additional 1D array with random probing to create a more robust technique that competes effectively with Cuckoo Hashing. This study also introduces degree of dexterity as a new performance metric, in addition to the traditional load factor. Furthermore, the Even-Odd hash function is proposed to ensure a more balanced load distribution. Through rigorous experimental analysis in a single-threaded environment, this modified Matrix hashing with random probing in the 1D array is shown to effectively resolve key issues associated with Cuckoo Hashing, such as excessive data migration, inefficient memory usage, and high insertion latency.