Need help to resolve Excel Formula using Let,Take,index,Sort,Unique,HSTACK,MMULT,TOROW,MONTH.

Norman_McIlwaine 

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Back to the sample, I added headers for better understanding, in general you may ignore them.

I guess we need to sum amount for identical Id, Date, Transaction and Type. That could be done by

=LET(
    range, $B$2:$G$10,
    Id, CHOOSECOLS(range, 1),
    date, CHOOSECOLS(range, 2),
    transaction, CHOOSECOLS(range, 4),
    type, CHOOSECOLS(range, 5),
    amount, CHOOSECOLS(range, 6),
    groupIndexes, {1,2,4,5},
    group, UNIQUE( CHOOSECOLS(range, groupIndexes ) ),
    VSTACK({"Id","Date","Transaction","Type","Amount"},
    HSTACK(
        group,
        BYROW( group,
            LAMBDA(v, SUM(
                FILTER(amount,
                    (Id = INDEX(v,1,1) )*
                    (date = INDEX(v,1,2) )*
                    (transaction = INDEX(v,1,3) )*
                    (type = INDEX(v,1,4) )
                )
            ) )
        )
    ) )
)

If we would like to filter for the specific year and month as they are defined here

slightly modified formula will be

=LET(
    range, $B$2:$G$10,
    year, $J$14,
    monthNumber, $J$15,
    Id, CHOOSECOLS(range, 1),
    date, CHOOSECOLS(range, 2),
    transaction, CHOOSECOLS(range, 4),
    type, CHOOSECOLS(range, 5),
    amount, CHOOSECOLS(range, 6),
    monthRange, FILTER(range, EOMONTH(date,0) = EOMONTH( DATE(year,monthNumber,1), 0 )),
    groupIndexes, {1,2,4,5},
    group, UNIQUE( CHOOSECOLS(monthRange, groupIndexes ) ),
    VSTACK({"Id","Date","Transaction","Type","Amount"},
    HSTACK(
        group,
        BYROW( group,
            LAMBDA(v, SUM(
                FILTER(amount,
                    (Id = INDEX(v,1,1) )*
                    (date = INDEX(v,1,2) )*
                    (transaction = INDEX(v,1,3) )*
                    (type = INDEX(v,1,4) )
                )
            ) )
        )
    ) )
)

Your initial formula sum amounts for the unique Id (only one column) in a given month. It's can't be adjusted directly for the few unique columns.

Another way is to create PivotTable, something like

Please check in attached file if that close to what you'd like to receive.