-- -*- M2-comint -*- {* hash: -1759787518 *}

i1 : R = ZZ/32003[a..f];

i2 : M = genericMatrix(R,a,3,2)

o2 = | a d |
     | b e |
     | c f |

             3       2
o2 : Matrix R  <--- R

i3 : N = matrix{{d^2,a*d},{b*c,b*d},{a,c}}

o3 = | d2 ad |
     | bc bd |
     | a  c  |

             3       2
o3 : Matrix R  <--- R

i4 : M|N

o4 = | a d d2 ad |
     | b e bc bd |
     | c f a  c  |

             3       4
o4 : Matrix R  <--- R

i5 : P = matrix{{d^2,a*d,e*f},{b*c,b*d,b*e},{a,c,d}}

o5 = | d2 ad ef |
     | bc bd be |
     | a  c  d  |

             3       3
o5 : Matrix R  <--- R

i6 : transpose(M)||P

o6 = {-1} | a  b  c  |
     {-1} | d  e  f  |
     {0}  | d2 ad ef |
     {0}  | bc bd be |
     {0}  | a  c  d  |

             5       3
o6 : Matrix R  <--- R

i7 : matrix{{id_(R^3),M,P},{random(R^1,R^3),random(R^1,R^3),random(R^1,R^2)}}

o7 = | 1      0     0     a     d    d2    ad     ef    |
     | 0      1     0     b     e    bc    bd     be    |
     | 0      0     1     c     f    a     c      d     |
     | -14215 14276 -9343 -2513 9387 -6475 -11220 14456 |

             4       8
o7 : Matrix R  <--- R

i8 :