Denote by 
the set of all 2×2 matrices with real number entries. Let ![M = \left[ {1 \atop 0} {1 \atop 1} \right]](https://web.archive.org/web/20170423155934im_/https://s0.wp.com/latex.php?latex=M+%3D+%5Cleft%5B+%7B1+%5Catop+0%7D+%7B1+%5Catop+1%7D+%5Cright%5D&bg=ffffff&fg=000000&s=0 "M = \left[ {1 \atop 0} {1 \atop 1} \right]")
and let 
.
Prove that if
, then 
, where juxtaposition denotes the usual matrix product.
Recall that matrix multiplication is associative. Then we have
, and thus . 
the set of all 2×2 matrices with real number entries. Let and let .Prove that if
, then , where juxtaposition denotes the usual matrix product.Recall that matrix multiplication is associative. Then we have
, and thus . 
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