I was looking into this and loved the approach from peege using a for loop! (because I'm learning VBA at the moment)
However, if we are trying to match "any" value of another column, how about using nested loops like the following?
Sub MatchAndColor()
Dim lastRow As Long
Dim sheetName As String
sheetName = "Sheet1" 'Insert your sheet name here
lastRow = Sheets(sheetName).Range("A" & Rows.Count).End(xlUp).Row
For lRowA = 1 To lastRow 'Loop through all rows
For lRowB = 1 To lastRow
If Sheets(sheetName).Cells(lRowA, "A") = Sheets(sheetName).Cells(lRowB, "B") Then
Sheets(sheetName).Cells(lRowA, "A").Interior.ColorIndex = 3 'Set Color to RED
End If
Next lRowB
Next lRowA
End Sub