Electrical Engineering > GATE 2026 > Matrix Algebra
Consider an n × n orthogonal matrix A with real entries and each column having unit Euclidean norm.
Which of the following statements is/are correct?
A
The value of the determinant of A is either +1 or −1
B
The eigenvalues of A have modulus 1
C
∥Ax∥ = ∥x∥, for all x∈Rn, and (Ax)T(Ay) ≠ xTy, for all distinct x,y∈Rn
D
∥Ax∥ = ∥x∥, for all x∈Rn, and (Ax)T(Ay) = xTy, for all x,y∈Rn

Correct : a,b,d

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