Matrix formating

hi,
I am working on one matrix problem and not able to design good algorithm for that one
here is problem.....
it's n*n matrix with following condition
1) Matrix contains 1...n2 elements exactly once
2) m[i,k] + m[i,l] = m[i,l] + m [j,k] where i,j,k,l = 1.....n
can any one give me good algo plz...........

Start by figuring out what the homework is asking you to do.
For instance, what should this algorithm do - construct such a matrix?, verify that a matrix is of the correct type? something else?
Condition (2) looks rather bizarre if i,j,k,l are allowed to have all values over the range 1...n. Cancelling the m[i,l] terms would leave the rows (or columns) consisting of a single element repeated n times.

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    </Textbox>
    </CellContents>
    </TablixHeader>
    <TablixMembers>
    <TablixMember>
    <Group Name="Month">
    <GroupExpressions>
    <GroupExpression>=Fields!Month.Value</GroupExpression>
    </GroupExpressions>
    </Group>
    <SortExpressions>
    <SortExpression>
    <Value>=Fields!Month.Value</Value>
    </SortExpression>
    </SortExpressions>
    <TablixHeader>
    <Size>0.25in</Size>
    <CellContents>
    <Textbox Name="Month">
    <CanGrow>true</CanGrow>
    <KeepTogether>true</KeepTogether>
    <Paragraphs>
    <Paragraph>
    <TextRuns>
    <TextRun>
    <Value>=MonthName(Fields!Month.Value)</Value>
    <Style>
    <FontFamily>Calibri</FontFamily>
    </Style>
    </TextRun>
    </TextRuns>
    <Style>
    <TextAlign>Center</TextAlign>
    </Style>
    </Paragraph>
    </Paragraphs>
    <rd:DefaultName>Month</rd:DefaultName>
    <Style>
    <Border>
    <Color>LightGrey</Color>
    <Style>Solid</Style>
    </Border>
    <PaddingLeft>2pt</PaddingLeft>
    <PaddingRight>2pt</PaddingRight>
    <PaddingTop>2pt</PaddingTop>
    <PaddingBottom>2pt</PaddingBottom>
    </Style>
    </Textbox>
    </CellContents>
    </TablixHeader>
    <TablixMembers>
    <TablixMember>
    <Group Name="GroupType">
    <GroupExpressions>
    <GroupExpression>=Fields!GroupType.Value</GroupExpression>
    </GroupExpressions>
    </Group>
    <SortExpressions>
    <SortExpression>
    <Value>=Fields!Month.Value</Value>
    </SortExpression>
    </SortExpressions>
    <TablixHeader>
    <Size>0.25in</Size>
    <CellContents>
    <Textbox Name="GroupType">
    <CanGrow>true</CanGrow>
    <KeepTogether>true</KeepTogether>
    <Paragraphs>
    <Paragraph>
    <TextRuns>
    <TextRun>
    <Value>=Fields!GroupType.Value</Value>
    <Style>
    <FontFamily>Calibri</FontFamily>
    </Style>
    </TextRun>
    </TextRuns>
    <Style>
    <TextAlign>Center</TextAlign>
    </Style>
    </Paragraph>
    </Paragraphs>
    <rd:DefaultName>GroupType</rd:DefaultName>
    <Style>
    <Border>
    <Color>LightGrey</Color>
    <Style>Solid</Style>
    </Border>
    <PaddingLeft>2pt</PaddingLeft>
    <PaddingRight>2pt</PaddingRight>
    <PaddingTop>2pt</PaddingTop>
    <PaddingBottom>2pt</PaddingBottom>
    </Style>
    </Textbox>
    </CellContents>
    </TablixHeader>
    </TablixMember>
    </TablixMembers>
    </TablixMember>
    </TablixMembers>
    </TablixMember>
    </TablixMembers>
    </TablixColumnHierarchy>
    <TablixRowHierarchy>
    <TablixMembers>
    <TablixMember>
    <Group Name="Name">
    <GroupExpressions>
    <GroupExpression>=Fields!Name.Value</GroupExpression>
    </GroupExpressions>
    </Group>
    <SortExpressions>
    <SortExpression>
    <Value>=Fields!Name.Value</Value>
    </SortExpression>
    </SortExpressions>
    <TablixHeader>
    <Size>1.16667in</Size>
    <CellContents>
    <Textbox Name="Name">
    <CanGrow>true</CanGrow>
    <KeepTogether>true</KeepTogether>
    <Paragraphs>
    <Paragraph>
    <TextRuns>
    <TextRun>
    <Value>=Fields!Name.Value</Value>
    <Style>
    <FontFamily>Calibri</FontFamily>
    </Style>
    </TextRun>
    </TextRuns>
    <Style />
    </Paragraph>
    </Paragraphs>
    <rd:DefaultName>Name</rd:DefaultName>
    <Style>
    <Border>
    <Color>LightGrey</Color>
    <Style>Solid</Style>
    </Border>
    <PaddingLeft>2pt</PaddingLeft>
    <PaddingRight>2pt</PaddingRight>
    <PaddingTop>2pt</PaddingTop>
    <PaddingBottom>2pt</PaddingBottom>
    </Style>
    </Textbox>
    </CellContents>
    </TablixHeader>
    </TablixMember>
    </TablixMembers>
    </TablixRowHierarchy>
    <DataSetName>DataSet1</DataSetName>
    <Top>0.49875in</Top>
    <Left>0.4675in</Left>
    <Height>1in</Height>
    <Width>2.16667in</Width>
    <Style>
    <Border>
    <Style>None</Style>
    </Border>
    </Style>
    </Tablix>
    </ReportItems>
    <Height>2in</Height>
    <Style />
    </Body>
    <Width>6.5in</Width>
    <Page>
    <LeftMargin>1in</LeftMargin>
    <RightMargin>1in</RightMargin>
    <TopMargin>1in</TopMargin>
    <BottomMargin>1in</BottomMargin>
    <Style />
    </Page>
    <AutoRefresh>0</AutoRefresh>
    <DataSources>
    <DataSource Name="AdventureWorks2012">
    <DataSourceReference>AdventureWorks2012</DataSourceReference>
    <rd:SecurityType>None</rd:SecurityType>
    <rd:DataSourceID>484e6561-ee09-4a7e-ad66-82f98face825</rd:DataSourceID>
    </DataSource>
    </DataSources>
    <DataSets>
    <DataSet Name="DataSet1">
    <Query>
    <DataSourceName>AdventureWorks2012</DataSourceName>
    <CommandText>SELECT
    'Invoice' AS GroupType,
    DATEPART(qq, soh.OrderDate) AS [Quarter],
    MONTH(soh.OrderDate) AS [Month],
    st.Name,
    SUM(soh.TotalDue) AS Amount
    FROM
    Sales.SalesOrderHeader AS soh
    JOIN Sales.SalesTerritory AS st
    ON soh.TerritoryID = st.TerritoryID
    WHERE
    year(soh.OrderDate) = 2008
    GROUP BY
    DATEPART(qq, soh.OrderDate),
    MONTH(soh.OrderDate),
    st.Name
    UNION ALL
    SELECT
    'Applied' AS GroupType,
    DATEPART(qq, soh.ShipDate) AS [Quarter],
    MONTH(soh.ShipDate) AS [Month],
    st.Name,
    SUM(soh.SubTotal) AS Amount
    FROM
    Sales.SalesOrderHeader AS soh
    JOIN Sales.SalesTerritory AS st
    ON soh.TerritoryID = st.TerritoryID
    WHERE
    year(soh.ShipDate) = 2008
    GROUP BY
    DATEPART(qq, soh.ShipDate),
    MONTH(soh.ShipDate),
    st.Name</CommandText>
    </Query>
    <Fields>
    <Field Name="GroupType">
    <DataField>GroupType</DataField>
    <rd:TypeName>System.String</rd:TypeName>
    </Field>
    <Field Name="Quarter">
    <DataField>Quarter</DataField>
    <rd:TypeName>System.Int32</rd:TypeName>
    </Field>
    <Field Name="Month">
    <DataField>Month</DataField>
    <rd:TypeName>System.Int32</rd:TypeName>
    </Field>
    <Field Name="Name">
    <DataField>Name</DataField>
    <rd:TypeName>System.String</rd:TypeName>
    </Field>
    <Field Name="Amount">
    <DataField>Amount</DataField>
    <rd:TypeName>System.Decimal</rd:TypeName>
    </Field>
    </Fields>
    </DataSet>
    </DataSets>
    <rd:ReportUnitType>Inch</rd:ReportUnitType>
    <rd:ReportID>3523f80e-1b49-43df-a36c-d80292f6a41a</rd:ReportID>
    </Report>
    Jason Long

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