If A = [[2,3],[3,5]] find determinant of:
A²⁰²⁵ − 3A²⁰²⁴ + A²⁰²³

Solution:

Take A²⁰²³ common:

A²⁰²³(A² − 3A + I)

Now,

A² − 3A + I = 0

Using Cayley-Hamilton theorem,

Expression becomes:
A²⁰²³ × 0

So determinant becomes:
16

Answer: 16