GATE Electrical 2018 | Question: 44

Question

Let $A= \begin{bmatrix} 1 & 0 & -1 \\ -1 & 2 & 0 \\ 0 & 0 & -2 \end{bmatrix}$ and $B=A^3-A^2-4A+5I$, where $I$ is the $3 \times 3$ identify matrix. The determinant of $B$ is _______ (up to $1$ decimal place).

Answer 1

use matrix to find eigen values of A -> then just use this polynomial to find eigen value of B, you will get three EValues of A and then three EVs of B

all three EVs of B are 1 => |B|= 1*1*1 =1