> with(LinearAlgebra);

  [Add, Adjoint, BackwardSubstitute, BandMatrix, Basis, BezoutMatrix,

        BidiagonalForm, BilinearForm, CharacteristicMatrix,

        CharacteristicPolynomial, Column, ColumnDimension,

        ColumnOperation, ColumnSpace, CompanionMatrix,

        ConditionNumber, ConstantMatrix, ConstantVector,

        CreatePermutation, CrossProduct, DeleteColumn, DeleteRow,

        Determinant, DiagonalMatrix, Dimension, Dimensions,

        DotProduct, EigenConditionNumbers, Eigenvalues, Eigenvectors,

        Equal, ForwardSubstitute, FrobeniusForm, GaussianElimination,

        GenerateEquations, GenerateMatrix, GetResultDataType,

        GetResultShape, GivensRotationMatrix, GramSchmidt,

        HankelMatrix, HermiteForm, HermitianTranspose, HessenbergForm,

        HilbertMatrix, HouseholderMatrix, IdentityMatrix,

        IntersectionBasis, IsDefinite, IsOrthogonal, IsSimilar,

        IsUnitary, JordanBlockMatrix, JordanForm, LA_Main,

        LUDecomposition, LeastSquares, LinearSolve, Map, Map2,

        MatrixAdd, MatrixInverse, MatrixMatrixMultiply, MatrixNorm,

        MatrixScalarMultiply, MatrixVectorMultiply, MinimalPolynomial,

        Minor, Modular, Multiply, NoUserValue, Norm, Normalize,

        NullSpace, OuterProductMatrix, Permanent, Pivot, PopovForm,

        QRDecomposition, RandomMatrix, RandomVector, Rank,

        ReducedRowEchelonForm, Row, RowDimension, RowOperation,

        RowSpace, ScalarMatrix, ScalarMultiply, ScalarVector,

        SchurForm, SingularValues, SmithForm, SubMatrix, SubVector,

        SumBasis, SylvesterMatrix, ToeplitzMatrix, Trace, Transpose,

        TridiagonalForm, UnitVector, VandermondeMatrix, VectorAdd,

        VectorAngle, VectorMatrixMultiply, VectorNorm,

        VectorScalarMultiply, ZeroMatrix, ZeroVector, Zip]

> A:=Matrix([[1,2,3],[4,5,6]]);

                               [1    2    3]
                          A := [           ]
                               [4    5    6]

> Transpose(A);

                               [1    4]
                               [      ]
                               [2    5]
                               [      ]
                               [3    6]

> B:=<<1,1,1>>;

                                    [1]
                                    [ ]
                               B := [1]
                                    [ ]
                                    [1]

> Transpose(A.B);

                              [6    15]

> A.B;
> 

                                 [ 6]
                                 [  ]
                                 [15]

> C:=Matrix([[1,3],[4,7]]);

                                 [1    3]
                            C := [      ]
                                 [4    7]

> E:=MatrixInverse(C);

                              [-7/5    3/5 ]
                         E := [            ]
                              [4/5     -1/5]

> C.E;

                               [1    0]
                               [      ]
                               [0    1]

> E.C;

                               [1    0]
                               [      ]
                               [0    1]

> MatrixInverse(<<0,1>|<1,1>>);

                              [-1    1]
                              [       ]
                              [ 1    0]

>