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Joint Entrance Examination
Mathematics
Matrices and Determinants
Question 23
Question 23 of 472
Medium
MCQ
If
A
=
[
2
3
3
5
]
A=[\begin{array}{|ccc|}2 & 3 \\ 3 & 5\end{array}]
A
=
[
2
3
3
5
]
, then the determinant of the matrix
(
A
2025
−
3
A
2024
+
A
2023
)
({A}^{2025}-3{A}^{2024}+{A}^{2023})
(
A
2025
−
3
A
2024
+
A
2023
)
is
A
12
B
24
C
28
D
16
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Official solution
A
=
(
23
35
)
,
∣
A
∣
=
1
∣
A
2025
−
3
A
2024
+
A
2023
∣
=
∣
A
2023
∣
∣
A
2
−
3
A
+
I
∣
=
16
\begin{gathered} A=(2 3 \\ 3 5),|A|=1 \\ |{A}^{2025}-3{A}^{2024}+{A}^{2023}|=|{A}^{2023}||{A}^{2}-3A+I|=16 \end{gathered}
A
=
(
23
35
)
,
∣
A
∣
=
1
∣
A
2025
−
3
A
2024
+
A
2023
∣
=
∣
A
2023
∣∣
A
2
−
3
A
+
I
∣
=
16
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