Geodesic
Computation of the commutator of $2\times2$ matrices via six multiplications
Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 47 (2007) no. 9 Cet article a éte moissonné depuis la source Math-Net.Ru

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An algorithm for computing the commutator $AB-BA$ of $2\times2$ matrices $A$ and $B$ is proposed. The algorithm involves six multiplications. In the case of Hermitian $2\times2$ matrices, it involves six real multiplications. 
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     title = {Computation of the commutator of $2\times2$ matrices via six multiplications},
     journal = {\v{Z}urnal vy\v{c}islitelʹnoj matematiki i matemati\v{c}eskoj fiziki},
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A. Ya. Belyankov. Computation of the commutator of $2\times2$ matrices via six multiplications. Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 47 (2007) no. 9. http://geodesic.mathdoc.fr/item/ZVMMF_2007_47_9_a0/

[1] Strassen V., “Gaussian elimination is not optimal”, Numer. Math., 13:4 (1969), 354–356 | DOI | MR | Zbl