MatricesMedium
Question
If $A = \begin{bmatrix} 2 & 3 \\ 3 & 5 \end{bmatrix}$, then the determinant of the matrix ( $A^{2025} - 3{\text{ }A}^{2024} + A^{2023}$ ) is
Options
A.28
B.12
C.24
D.16
Solution
$A = \begin{bmatrix} 2 & 3 \\ 3 & 5 \end{bmatrix} \Rightarrow A^{2} = \begin{bmatrix} 13 & 21 \\ 21 & 34 \end{bmatrix}$
$$\begin{matrix} & \left| A^{2025} - 3A^{2024} + A^{2023} \right| \\ & \ = \left| A^{2023}\left( A^{2} - 3A + I \right) \right| \\ & \ = |A|^{2023}\left| A^{2} - 3A + I \right| \\ & \ = 1 \cdot \left| \begin{matrix} 8 & 12 \\ 12 & 20 \end{matrix} \right| = 160 - 144 = 16 \end{matrix}$$
Create a free account to view solution
View Solution FreeMore Matrices Questions
Which of the following is(are) NOT the square of a 3 ×3 matrix with real entries ?...Let $A = \begin{bmatrix} - 1 & 1 & - 1 \\ 1 & 0 & 1 \\ 0 & 0 & 1 \end{bmatrix}$ satisfy$A^{2} + ...If A =and X is a matrix such that A = BX, then X equals -...If A = , then A (adj A) equals -...If is square root of I2, then α, β and γ will satisfy the relation -...