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Technique

Matrix polynomial equations

A2(trA)A+AI=O(2×2)A^2 - (\operatorname{tr}A)\,A + |A|\,I = O \quad (2\times2)
AA
a square matrix
trA\operatorname{tr}A
the trace, sum of diagonal entries
II
the identity matrix

A matrix satisfying a polynomial equation can be rearranged to give its inverse, its powers, or an unknown coefficient. For order two this is the Cayley-Hamilton relation.

48
questions use it
28
of them past-year
2018–2026
years it has appeared
25%
rated HARD
3
exams
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Used alongside

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

48 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.

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