> 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 := <<a11,a21>|<a12,a22>>;

                               [a11    a12]
                          A := [          ]
                               [a21    a22]

> b := Vector([b1,b2]);

                                   [b1]
                              b := [  ]
                                   [b2]

> LinearSolve(A,b);

                        [   a12 b2 - a22 b1  ]
                        [- ------------------]
                        [  -a12 a21 + a22 a11]
                        [                    ]
                        [  a11 b2 - b1 a21   ]
                        [ ------------------ ]
                        [ -a12 a21 + a22 a11 ]

> MatrixInverse(A);

            [        a22                      a12        ]
            [ ------------------     - ------------------]
            [ -a12 a21 + a22 a11       -a12 a21 + a22 a11]
            [                                            ]
            [         a21                    a11         ]
            [- ------------------     ------------------ ]
            [  -a12 a21 + a22 a11     -a12 a21 + a22 a11 ]

>