some random matrix a:
0.543060 2.655328 9.561987 
7.341275 3.256728 4.575466 
8.628987 3.395740 1.309642 
6.955890 2.391436 8.528098 
3.876360 0.427608 8.127462 
[q,r]=qrdec(a)
q:
0.039186 0.901183 0.381850 
0.529729 0.172393 -0.162304 
0.622647 0.043580 -0.483191 
0.501921 -0.092148 0.361385 
0.279709 -0.384396 0.681011 
q^Tq:
1.000000 0.000000 0.000000 
0.000000 1.000000 0.000000 
0.000000 0.000000 1.000000 
r:
13.858543 5.263502 10.167653 
0.000000 2.717620 5.552937 
0.000000 0.000000 10.892633 
qr:
0.543060 2.655328 9.561987 
7.341275 3.256728 4.575466 
8.628987 3.395740 1.309642 
6.955890 2.391436 8.528098 
3.876360 0.427608 8.127462 
some random matrix a:
0.169885 5.606727 0.133627 4.501492 4.491991 
7.022715 2.768089 9.653150 5.400310 0.292874 
5.131104 5.650347 0.409409 4.406630 3.313001 
9.755361 9.774598 2.077450 2.078373 0.429678 
0.764993 0.014367 3.149899 3.831254 3.600066 
some random vector b:
6.795316 
2.897487 
9.113710 
9.964248 
7.342713 
solution to Ax=b:
1.254266 
-0.045515 
0.449078 
-2.068172 
3.581325 
Ax:
6.795316 
2.897487 
9.113710 
9.964248 
7.342713 
a^-1
-0.226619 -0.057106 0.164748 0.050736 0.129744 
0.200535 0.014198 -0.188953 0.092615 -0.088541 
0.073901 0.015145 -0.350777 0.155783 0.210771 
0.064472 0.238941 0.525154 -0.407435 -0.534534 
-0.085918 -0.255459 -0.286217 0.286145 0.635001 
a^-1a
1.000000 0.000000 0.000000 0.000000 0.000000 
-0.000000 1.000000 -0.000000 -0.000000 -0.000000 
0.000000 0.000000 1.000000 0.000000 0.000000 
-0.000000 -0.000000 -0.000000 1.000000 -0.000000 
0.000000 0.000000 0.000000 0.000000 1.000000 
aa^-1
1.000000 -0.000000 -0.000000 -0.000000 0.000000 
-0.000000 1.000000 -0.000000 0.000000 0.000000 
-0.000000 0.000000 1.000000 0.000000 0.000000 
-0.000000 -0.000000 0.000000 1.000000 0.000000 
-0.000000 0.000000 0.000000 0.000000 1.000000