Added Freivalds' Algorithm for randomized matrix multiplication verification

[aditya-7562]

Summary

Added Freivalds' Algorithm under the randomized category as part of issue [#6219]

This algorithm offers a fast, probabilistic method to verify whether matrix multiplication A × B = C holds true, avoiding full recomputation of the product.

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🧠 Randomized Algorithm Approach

• Generate a random binary vector r
• Perform matrix-vector multiplications and check if:
  A × (B × r) ≟ C × r
• Repeat this process k times to reduce the probability of error
• Probability of false positives becomes ≤ 1/2^k

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⏱ Time Complexity

• Per iteration: O(n²)
• Total expected time: O(k × n²)
  (significantly faster than recomputing A × B, which is O(n³))

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✅ Use Cases

• Verifying matrix multiplication in:
  • Scientific computing workflows
  • Distributed computing systems
  • Cloud infrastructure and audit pipelines
• Faster correctness checks in:
  • Numerical linear algebra
  • Cryptographic or zero-knowledge systems

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📋 Checklist

• I have read CONTRIBUTING.md
• This pull request is entirely my work (no plagiarism)
• All filenames follow PascalCase convention
• All function and variable names follow Java naming conventions
• Code has been formatted using:
  clang-format -i --style=file path/to/your/file.java

[codecov-commenter]

Codecov Report

All modified and coverable lines are covered by tests ✅

Project coverage is 74.37%. Comparing base (712ada5) to head (e1af216).

Additional details and impacted files

@@             Coverage Diff              @@
##             master    #6340      +/-   ##
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+ Coverage     74.33%   74.37%   +0.04%     
- Complexity     5392     5403      +11     
============================================
  Files           679      680       +1     
  Lines         18820    18842      +22     
  Branches       3646     3656      +10     
============================================
+ Hits          13990    14014      +24     
+ Misses         4274     4273       -1     
+ Partials        556      555       -1     

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[siriak]

Looks good, thanks!