GATE IN 2026 | Question: 1

Question

A matrix $P \in \mathbb{R}^{3 \times 3}$ satisfies $P^{3}-4 P^{2}+5 P-2 I=0$ where $I$ is a $3 \times 3$ identity matrix.

The set of all possible eigenvalues of matrix $P$ is $\_\_\_\_\_\_$ .

• A. $\{1,2,3\}$
• B. $\{1\}$
• C. $\{1,2\}$
• D. $\{2\}$

Answer 1

just Subtitute the given set of value

For i = 1

1 - 4 + 5 -2 = 0

For i = 2.

8 - 16 + 10 - 2  = 0

So option C is correct .