Bourbaki

Exercise 3, § 2

Functions of a Real Variable, IV, 204

Given the two matrices

A=(0100),B=(0010) A = \begin{pmatrix} 0 & 1 \\ 0 & 0 \end{pmatrix}, \qquad B = \begin{pmatrix} 0 & 0 \\ 1 & 0 \end{pmatrix}
show that exp⁡(A+B)≠exp⁡(A)exp⁡(B)\exp(A + B) \neq \exp(A) \exp(B).

Solution

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Transcribed from the printed volume. Not translated.