Prove that every real matrix that commutes with the matrix \[ A:=\begin {bmatrix} 1 & 2\\ 3 & 4 \end {bmatrix} \] is of the form \(rI+sA\), for some real numbers \(r,s\).
Question
Math 6310 • Algebra
Fall 2017 • Question 7
Question
Fall 2017 • Question 7
Prove that every real matrix that commutes with the matrix \[ A:=\begin {bmatrix} 1 & 2\\ 3 & 4 \end {bmatrix} \] is of the form \(rI+sA\), for some real numbers \(r,s\).