UPSC NDA I 2025 Mathematics Paper

Statement I
|M2|=|M×M|=|M|⋅|M|=|M|2
⇒ Statement I is correct.
Statement II
For a non-singular matrix, M×M−1=I, where I is the identity matrix.
|M|⋅|M−1|=|I|=1
⇒ Statement II is incorrect unless |M|=±1.
Statement III
The determinant of a matrix is equal to the determinant of its transpose:
|M|=|MT|
⇒ Statement III is correct.
Out of the three statements, two are correct: I and III.