Solution

The correct answer is option 4.

Key Points

\(\left[ {\begin{array}{*{20}{c}} 2&0&0\\ 0&2&0\\ 0&0&1 \end{array}} \right]\) It is the scaling matrix. 2 in x and y-direction by a factor,

Hence A-II is the correct pair.
\(\left[ {\begin{array}{*{20}{c}} 1&0&2\\ 0&1&2\\ 0&0&1 \end{array}} \right]\) is the translation matrix. Vector 2 in each direction of x and y

Hence  B-IV is the correct pair
\(\left[ {\begin{array}{*{20}{c}} {0.5}&{ - 0.866}&0\\ {0.866}&{0.5}&0\\ 0&0&1 \end{array}} \right]\)is an angle of 60 degrees rotation matrix.

Hence  C-III is the correct pair
\(\left[ {\begin{array}{*{20}{c}} 1&2&0\\ 0&1&0\\ 0&0&1 \end{array}} \right]\)is the shear matrix of quantity 2 with only x-shear.

Hence  D-I is the correct pair

∴ Hence the correct answer is A-II, B - IV, C - III, D - I.