> 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, 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, Multiply, NoUserValue, Norm, Normalize, NullSpace,

        OuterProductMatrix, Permanent, Pivot, 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 :=<<1,2>|<3,4>>;

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

> B := <<1,2>|<3,5>>;

                                 [1    3]
                            B := [      ]
                                 [2    5]

> A=B;

                         [1    3]   [1    3]
                         [      ] = [      ]
                         [2    4]   [2    5]

> Equal(A,B);

                                false

> B[2,2]:=4;

                             B[2, 2] := 4

> Equal(A,B);

                                 true

> ?MatrixAdd
> A + B;

                               [2    6]
                               [      ]
                               [4    8]

> C := <<a,b>|<c,d>>;

                                 [a    c]
                            C := [      ]
                                 [b    d]

> A + C;

                           [1 + a    3 + c]
                           [              ]
                           [2 + b    4 + d]

> C + B;

                           [1 + a    3 + c]
                           [              ]
                           [2 + b    4 + d]

> alpha*
> A;

                                  [1    3]
                            alpha [      ]
                                  [2    4]

> ?MatrixScalarMultiply
> ScalarMultiply(A,alpha);

                         [ alpha     3 alpha]
                         [                  ]
                         [2 alpha    4 alpha]

> ScalarMultiply(B, 7);

                              [ 7    21]
                              [        ]
                              [14    28]

>