TITLE: A problem on linear algebra
QUESTION [6 upvotes]: If $M$ is a $3 \times 3$ matrix such that
$$[ 0 ~~1 ~~2 ]M = [ 1 ~~0~~ 0 ] \text{  and  } [ 3~~ 4 ~~5 ]M = [ 0 ~~1 ~~0 ]$$
then what is the value of $[ 6 ~~7 ~~8 ]M$ ?
I guess some matrix property needs to be used.

REPLY [11 votes]: Hint: $[6~ 7 ~8]=2[3~ 4~ 5]-[0~ 1 ~2]$.