I need a complete project in Matlab i give you all details. The project topic is Gaussian Elimination of Rook Pivoting. I read few research papers and I think some changes or improve those research papers. Some research paper focuses on comparing the computational cost, stability, and efficiency of different pivoting strategies, particularly rook pivoting and partial pivoting, in the context of Gaussian elimination. If I want to enhance the discussion, particularly in relation to the term "flop" $($floating$-$point operations$),$ here are some ideas:

Detailed Flop Count: Provide a more detailed breakdown of the FLOP count for each pivoting strategy. Specify the number of FLOPs involved in different stages of the Gaussian elimination process, such as forward elimination and back$-$substitution

Quantitative Analysis of Flops: Provide a more detailed quantitative analysis of the floating$-$point operations $($FLOPs$)$ involved in each pivoting strategy. Compare the actual number of FLOPs required for rook pivoting and partial pivoting, highlighting the computational cost difference.

Flop Count in Different Phase: Break down the FLOP count into different phases of the Gaussian elimination process. Analyze the contributions of each phase to the overall computational cost and identify areas where optimizations can be applied. Now i need to Introduce Gaussian Elimination with Rook Pivoting, i can analyze the $3$ methods, give some examples, and discuss the advantages and disadvantages of each of the $3$ methods. Please implement the methods using Matlab scripts $($not the built$-$in Matlab functions$).$ and also added a best conclusion please with some references.