No, they are called absolute references.
Relative cell references and some mixed cell references will change when a formula is copied.
Excel uses relative (A2), absolute ($A$2), and mixed ($A2) cell references.
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You can do this using relative reference.
relative cell address
Yes, you can use as many combinations of absolute and relative references as you like on the same worksheet.
It contains relative cell references.
Cell references in a formula don't change if they are moved. Relative references will change if they are copied. Mixed references may change, depending on the type of mixed reference and which direction they are copied.
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Use absolute references (e.g. $C$3) instead of relative references (e.g. C3). See related questions for more information about absolute references.