IITB Practice Set: 15

Question

Suppose G is a $\textit{group}$ formed by all $2\times 2$ matrices with the group operation being matrix addition. Which
all of the following are subgroups of $G$?

• A. The set of all $2\times 2$ invertible matrices.
• B. The set of all $2\times 2$ symmetric matrices.
• C. The set of all $2\times 2$ matrices with the top right entry being $0$.
• D. The set of all $2\times2$ matrices with the top right entry being $1$.

Comments

Here, identity element(e) is null matrix. e must belongs to the group set. Determinant(null matrix)=0 so not invertible and all elements are zero. So option A and D eliminated.