Discussion
The constraint \(A^{2} = A\) on any square matrix A is satisfied for
Answer: C
The constraint holds for both the identity matrix and the null matrix.
A matrix with \(A^{2} = A\) is called idempotent. For the identity, \(I^{2} = I \cdot I = I\); for the null matrix, \(O^{2} = O\). So both satisfy the constraint, and the options saying 'the identity matrix only' or 'the null matrix only' each leave out a matrix that works.
'No square matrix' is plainly false. Other idempotent matrices also exist (any projection matrix, such as \(\begin{bmatrix} 1 & 0 \\ 0 & 0 \end{bmatrix}\)), but among the four options the only one that is true is the one naming both the identity and the null matrix.
No comment is present. Be the first to comment.
Loading…
Post your comment
Please log in or register to post a comment.
Examination Categories
- SSC Exams
- Banking Exams
- Teaching Exams
- Civil Services Exams
- Railways Exams
- Engineering Recruitment Exams
- Defence Exams
- State Government Exams
- Police Exams
- Insurance Exams
- Nursing Exams
- Other Government Exams
- NRA CET
- PG Entrance Exams
- Campus Placement
- MBA Entrance Exams
- CUET and UG Entrance
- Judiciary Exams
- Regulatory Body Exams
- Software Development