Question

If the matrices $\left(\begin{matrix} 1 & 0 \\   0 & 0  \end{matrix}\right),\left(\begin{matrix}   -1 & 0 \\   0 & 0  \end{matrix}\right),\left(\begin{matrix}   i & 0 \\   0 & 0  \end{matrix}\right) and \left(\begin{matrix}   -i & 0 \\   0 & 0  \end{matrix}\right)$ form a group with respect to matrix multiplication, then which one of the following statements about the groups, thus formed is correct?

• A. The group has no element of order 4.
• B. The group has an element of order 3.
• C. The group is non-abelian
• D. $\left(\begin{matrix} -1 & 0 \\   0 & 0  \end{matrix}\right)$is its own inverse

Answer 1

The Correct Option is D

The correct answer is(D): $\left(\begin{matrix} -1 & 0 \\   0 & 0  \end{matrix}\right)$is its own inverse