I need an assist with a programming logic math question.

I need an assist with a programming logic math question.
Here is a simple array of 8 rows &  8 cols.   True/false 1/0

I need to find the group of 8 RnCn's which are all 0's, but do not share the same R or C , i.e. no horizontal or vertical duplicates.

I had to figure this out manually.  There are 2 groups left, then the array will be all 1s.

1st remaining group is:     R1C7   R2C4   R3C3  R4C6  R5C5  R6C2  R7C1  R8C8
2nd remaining group is:    R1C8   R2C2   R3C6  R4C4  R5C3  R6C1  R7C7  R8C5

The QUESTION is:  Can you share with me how to program code (such as VBA or VS)  to find these 2 groups ??

  1  1  1  1  1  1  0  0 
  1  0  1  0  1  1  1  1 
  1  1  0  1  1  0  1  1 
  1  1  1  0  1  0  1  1 
  1  1  0  1  0  1  1  1 
  0  0  1  1  1  1  1  1 
  0  1  1  1  1  1  0  1 
  1  1  1  1  0  1  1  0 

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Such as:

Dim MyGroupByRow(8)  = 0 
For r = 1 to 8
    For c = 1 to 8  
        If RowCol(r,c) = 0   And   MyGroupByRow(r)  = 0  Then 
            ' 1st col found in row = 1 is c = 7.     r2 will be=2  r3=3, r4=4, r5=5, r6=1, r7=?
            MyGroupRow(r) = c
            Exit For   ' We're done with this row, exit this For c = loop and go to next r.
        End If
    Next
Next

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The problem starts at r = 7 because I can't find a still available column which is 0 and not already taken in MyGroupRow().
You just can't the 1st column with a 0 in each row.  
How do I program some sort of deeper iteration code logic to find the right group?