1.6.35 Fields, Groups, Rings

Condition: Find out whether the algebraic system \( (u, \bigoplus, \otimes) \) is a ring or a field, where \( u=\left\{\left(\begin{array}{ll}a & 0 \\ 0 & b\end{array}\right) \mid a, b \in R\right\}, \bigoplus \)-matrix addition, \( \otimes \)-matrix multiplication.