MathDB
Determinant of a certain kind of matrix

Source: IMC 2007 Day 2 Problem 4

August 7, 2007
linear algebramatrixmodular arithmeticinductiontrigonometryinequalitiesalgebra

Problem Statement

Let n>1 n > 1 be an odd positive integer and A=(aij)i,j=1..n A = (a_{ij})_{i, j = 1..n} be the n×n n \times n matrix with aij={2if i=j1if i−j≡±2(modn)0otherwise. a_{ij}= \begin{cases}2 & \text{if }i = j \\ 1 & \text{if }i-j \equiv \pm 2 \pmod n \\ 0 & \text{otherwise}\end{cases}. Find det⁡A \det A.
Back to ProblemsView on AoPS