The GATE Grind

GATE 2026 CE (CE1) – Question 11

Engineering Mathematics · Linear Algebra: Matrix algebra, systems of linear equations, eigenvalues and eigenvectors · 1 mark · Multiple choice

Matrix $P$ is given as

$$P = \begin{bmatrix} 1 & 0 & 1 \\ 0 & 1 & 0 \\ 1 & 0 & 1 \end{bmatrix}$$

The TRUE option is

  1. Trace of $P$ is equal to the sum of the Eigen values of $P$.
  2. $P^TP$ is an identity matrix.
  3. $P$ is a skew-symmetric matrix.
  4. Absolute magnitude of each Eigen value is 1.

Practise this question in The GATE Grind →

Show answer and explanation

Correct answer: (A) Trace of $P$ is equal to the sum of the Eigen values of $P$.

Explanation

The sum of the eigenvalues of any square matrix equals its trace, so A is always true. Here the eigenvalues are 2, 1 and 0, which add up to the trace 3. $P^TP$ is not the identity, $P$ is symmetric and not skew-symmetric, and the eigenvalues 2 and 0 do not have magnitude 1.