Option A). It is clearly false
since Rank of the Matrix = at most min(number of column,number of rows).
so it will be at most 11.
Option B). It is kind of a hypocritical statement.
To find rank we are doing Gaussian elimination to convert matrix into row echelon form or simply we are doing row operations only.
so it simply doesn’t affect the rank.
Option C). True Rank isn’t affected by row operation, the number of pivots and number of free variables will remain the same.
Option D). True already mentioned in option A.