QR decomposition with Givens rotations:
random matrix A:
     0.348      1.379      1.500 
     0.409      2.106      3.199 
     0.585      0.998      2.550 
     1.922      1.430      5.791 
     1.816      3.559      0.670 
copy of A:
     0.348      1.379      1.500 
     0.409      2.106      3.199 
     0.585      0.998      2.550 
     1.922      1.430      5.791 
     1.816      3.559      0.670 
R=
     2.761      4.034      5.676 
     0.000      2.403     -0.366 
     0.000      0.000      4.541 
Q=
     0.126      0.363      0.202 
     0.148      0.627      0.570 
     0.212      0.059      0.301 
     0.696     -0.574      0.359 
     0.658      0.377     -0.644 

testing Q^T*Q == 1 ?
Q.t*Q=
     1.000     -0.000      0.000 
    -0.000      1.000     -0.000 
     0.000     -0.000      1.000 
test passed

testing Q*R == A ?
QR=
     0.348      1.379      1.500 
     0.409      2.106      3.199 
     0.585      0.998      2.550 
     1.922      1.430      5.791 
     1.816      3.559      0.670 
test passed

testing inverse
random square matrix A:
     0.773      1.615      2.048 
     1.235      0.339      3.342 
     0.693      0.022      4.286 
inverse=
    -0.331      1.649     -1.128 
     0.714     -0.454      0.013 
     0.050     -0.264      0.415 
testing A*inverse == 1 ?
A*inverse=
     1.000      0.000      0.000 
     0.000      1.000     -0.000 
     0.000     -0.000      1.000 
test passed
testing inverse*A == 1 ?
inverse*A=
     1.000      0.000     -0.000 
    -0.000      1.000      0.000 
    -0.000     -0.000      1.000 
test passed