Math Problem Statement
Let A be a 2x2 matrix with integer such that A^2 = 3A and det(A) = 6. Consider the matrix A reduced modulo 7. Determine how many distinct values the trace of the resulting matrix can take.
Solution
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Math Problem Analysis
Mathematical Concepts
Linear Algebra
Eigenvalues and Eigenvectors
Determinants
Modular Arithmetic
Formulas
Matrix polynomial equation A^2 = 3A
Determinant formula det(A) = product of eigenvalues
Theorems
Eigenvalue theorem for matrices
Properties of determinants and trace under modular reduction
Suitable Grade Level
College Level