Geodesic
Computation of the commutator of $2\times2$ matrices via five multiplications
Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 48 (2008) no. 2, pp. 201-205

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Algorithms for computing the commutator $AB$–$BA$ of $2\times2$ matrices $A$ and $B$ are proposed that involve five multiplications. 
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     author = {A. Ya. Belyankov},
     title = {Computation of the commutator of $2\times2$ matrices via five multiplications},
     journal = {\v{Z}urnal vy\v{c}islitelʹnoj matematiki i matemati\v{c}eskoj fiziki},
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     publisher = {mathdoc},
     volume = {48},
     number = {2},
     year = {2008},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZVMMF_2008_48_2_a1/}
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A. Ya. Belyankov. Computation of the commutator of $2\times2$ matrices via five multiplications. Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 48 (2008) no. 2, pp. 201-205. http://geodesic.mathdoc.fr/item/ZVMMF_2008_48_2_a1/