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?
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?
Updated On: Mar 12, 2025
- The group has no element of order 4.
- The group has an element of order 3.
- The group is non-abelian
- \(\left(\begin{matrix} -1 & 0 \\ 0 & 0 \end{matrix}\right)\)is its own inverse
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The Correct Option is D
Solution and Explanation
The correct answer is(D): \(\left(\begin{matrix} -1 & 0 \\ 0 & 0 \end{matrix}\right)\)is its own inverse
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