Let ![S=\left\{\begin{array}{c}\left[\begin{array}{cc}a_{11}&a_{12}\\a_{21}&a_{22}\end{array}\right]:a_{ij}\ \epsilon\ \{0,1,2\},a_{11}=a_{22}\end{array}\right\}](https://tex.z-dn.net/?f=S%3D%5Cleft%5C%7B%5Cbegin%7Barray%7D%7Bc%7D%5Cleft%5B%5Cbegin%7Barray%7D%7Bcc%7Da_%7B11%7D%26amp%3Ba_%7B12%7D%5C%5Ca_%7B21%7D%26amp%3Ba_%7B22%7D%5Cend%7Barray%7D%5Cright%5D%3Aa_%7Bij%7D%5C+%5Cepsilon%5C+%5C%7B0%2C1%2C2%5C%7D%2Ca_%7B11%7D%3Da_%7B22%7D%5Cend%7Barray%7D%5Cright%5C%7D+ "S=\left\{\begin{array}{c}\left[\begin{array}{cc}a_{11}&a_{12}\\a_{21}&a_{22}\end{array}\right]:a_{ij}\ \epsilon\ \{0,1,2\},a_{11}=a_{22}\end{array}\right\}")
. Then the number of non-singular matrices in the set S is:
(a) 27
(b) 24
(c) 10
(d) 20
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