NDA 2025 Maths · Mathematics · Matrices · hard

Let A be a 2×2 real matrix with A^2=I and A≠± I. Then tr(A) equals

Single correct option

Let

A

be a

2\times2

real matrix with

A^2=I

and

A\ne\pm I

. Then

\operatorname{tr}(A)

equals

Show answer and solution

Answer: (A) $0$

A^2=I

gives

(A-I)(A+I)=O

. As

A\ne\pm I

, neither factor is zero, so the eigenvalues are

1

and

-1

(both occur). The trace is their sum,

0

. Example:

A=\operatorname{diag}(1,-1)

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