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the conversion factor merely changes the number in such a way that it fits the new units the physical quantity is not changed

Q: Why is the fundamental value of a quantity not changed when the quantity is multiplied by a conversion factor?

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Not a fixed quantity. By the time you get to read this, it will have changed. Try number of complete days to go, multiplied by 24, plus number of hours and minutes left in the day at the time you read this.

An eigenvector is a vector which, when transformed by a given matrix, is merely multiplied by a scalar constant; its direction isn't changed. An eigenvalue, in this context, is the factor by which the eigenvector is multiplied when transformed.

The associative property.

No, only the units of measurement are changed.

When dividing by a fraction, the second fraction (the divisor) is changed into its reciprocal by swapping the numerator and denominator over (turning it upside down) and then it is multiplied by the first number (fraction).

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Not a fixed quantity. By the time you get to read this, it will have changed. Try number of complete days to go, multiplied by 24, plus number of hours and minutes left in the day at the time you read this.

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If the length and width of a rectangle are both multiplied by K, then the originalperimeter is multiplied by K, and the area is multiplied by K2 .

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The area is multiplied by 4, not doubled.

The total energy of a closed system remains constant when the state is changed. This is described by the first law of thermodynamics, which states that energy cannot be created or destroyed, only transferred or converted from one form to another.

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The simple is that fundamental quantities can be changed its not constant always and derived Quantities is like to constant always it could not be change ever.