Teaching MPPSC Assistant Professor Mock Test Series 2025 Mathematical Science Algebra Integral Domain & its types
Which one of the following ring of matrix is not a field?
1
\(\{(\begin{smallmatrix} a&b \\ 2b&a \end{smallmatrix} \bigr) : a, b \in \mathbb Q \}\)
2
\(\{(\begin{smallmatrix} a&b \\ 2b&a \end{smallmatrix} \bigr) : a, b \in \mathbb R \}\)
3
\(\{(\begin{smallmatrix} a&b \\ 3b&a \end{smallmatrix} \bigr) : a, b \in \mathbb Q \}\)
4
\(\{(\begin{smallmatrix} a&b \\ -b&a \end{smallmatrix} \bigr) : a, b \in \mathbb R \}\)