What is the Trace of matrix P in GATE Civil Engineering 2026 Set-1 Q11?

The trace of matrix P equals the sum of its Eigen values. Given options, this aligns with option A.

Is P T P an identity matrix in GATE Civil Engineering 2026 Set-1 Q11?

P T P is not necessarily the identity matrix. This can be verified by calculating P and its transpose.

Matrix P is not skew-symmetric. This can be determined by checking if P = -P T .

The absolute value of each Eigen value is not necessarily 1. This can be verified by calculating the Eigen values.

Civil Engineering > GATE 2026 SET-1 > Linear Algebra

Matrix P is given as

The TRUE option is

Trace of P is equal to the sum of the Eigen values of P.

P^TP is an identity matrix.

P is a skew-symmetric matrix.

Absolute magnitude of each Eigen value is 1.

Correct : a