The inverse of the 2 × 2 matrix \[\left[ {\begin{array}{*{20}{c}} 1&2 \\ 5&7 \end{array}} \right]\]  is

A. \[\frac{1}{3}\left[ {\begin{array}{*{20}{c}} { - 7}&2 \\ 5&{ - 1} \end{array}} \right]\]

B. \[\frac{1}{3}\left[ {\begin{array}{*{20}{c}} 7&2 \\ 5&1 \end{array}} \right]\]

C. \[\frac{1}{3}\left[ {\begin{array}{*{20}{c}} 7&{ - 2} \\ { - 5}&1 \end{array}} \right]\]

D. \[\frac{1}{3}\left[ {\begin{array}{*{20}{c}} { - 7}&{ - 2} \\ { - 5}&{ - 1} \end{array}} \right]\]

Answer: Option A