3

523458999999999999998777774361627493452+4^56

x

x+y

x+x

(v={{1,2,3}})//MatrixForm

Transpose[v]//MatrixForm

Transpose[Transpose[v]]

Transpose[Transpose[v1]]//FullSimplify

v1={{2,3,4}};
v2={{4,5,6}};

v1*v2

v1.Transpose[v2]

M1={{1,2,3},{2,3,4}};
M1//MatrixForm
Transpose[M1]//MatrixForm

Transpose[M]

Ma*Mb

Ma={{1,2},{3,4}};
Mb={{a,b},{c,d}};

Ma Mb//MatrixForm

MatrixForm/@{Ma,Mb,Ma.Mb}

MatrixForm/@{Mb,Ma,Mb.Ma}

{a+3 b}

Mc={{m,n},{p,q}};
Mb={{a,b},{c,d}};

MatrixForm/@{Mc,Mb,Mc.Mb}

{m a + n c}

A={{Atl,Atr},{Abl,Abr}};
B={{Bt},{Bb}};

A.B

P={{Dtl,Dtr},{Dbl,Dbr}};
Q={{Ct},{Cb}};

P.Q

?Random

MatrixForm[A=RandomInteger[{0,10},{4,3}]]
MatrixForm[B=RandomInteger[{0,10},{3,2}]]

Atl=A[[1;;3,1;;2]];Atr=A[[1;;3,3]];
Abl=A[[4,1;;2]];Abr=A[[4,3]];
Bt=B[[1;;2,1;;2]];Bb=B[[3,1;;2]];

A.B//MatrixForm

Atl.Bt

Atr

Atl.Bt+Atr.Bb