Kunze Linear Algebra · Problem 1.5.8

Systems of Linear Equations

Mathematics — Methods · commutator-matrices

Problem

Let

C = \begin{bmatrix} C_{11} & C_{12} \\ C_{21} & C_{22} \end{bmatrix}

be a

2 \times 2

matrix. We inquire when it is possible to find

2 \times 2

matrices

A

and

B

such that

C = AB - BA

. Prove that such matrices can be found if and only if

C_{11} + C_{22} = 0