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Technique

Powers of a matrix

An=AAAnA^n = \underbrace{A\cdot A\cdots A}_{n}
AA
a square matrix
nn
the exponent

High powers of a structured matrix are found by computing the first few and reading off the pattern, not by repeated multiplication.

54
questions use it
29
of them past-year
2015–2026
years it has appeared
17%
rated HARD
4
exams
Matrices & Determinants notesOpen all 54 in the paper builder

Used alongside

How often each of these appears in the same solution as this one.

54 questions whose solution uses this

Every one was read individually — a question is here because its solution invokes this, not because the stem mentions it.

Every identity this chapter tests, with its own question set.

All Matrices & Determinants formulas