In a rational number, what is the number whose reciprocal is itself? Is there a number whose square is equal to itself? What number is a cube equal to itself? Is there a number whose absolute value is equal to itself?

In a rational number, what is the number whose reciprocal is itself? Is there a number whose square is equal to itself? What number is a cube equal to itself? Is there a number whose absolute value is equal to itself?

The inverse is that its number is 1,-1.
The number whose square is equal to itself is 0,1
A cube has a number equal to itself 0,1,-1
The absolute value is equal to its own number 0 and a positive number (non-negative)

If the absolute value of a rational number and the sum of its reciprocal equals 0, then what is the number? If the absolute value of a rational number is equal to the sum of its reciprocal, then what is the number?

If the sum of a rational number and its reciprocal equals 0, then the number is -1,0
The absolute value of -1 is 1, the reciprocal of -1 is -1, and equals 0.
The absolute value of 0 is 0, the reciprocal of 0 is 0, and equals 0.