#### Answer

$\text{True}$

#### Work Step by Step

We know that an equation can be satisfied for every value of the variable when both sides of that equation are defined is called an identity.
$(x-1)^{2}-1=x(x-2)\\ x^{2}-2x+1-1=x^{2}-2x\\x^2-2x=x^2-2x$
We see that the equations are equivalent .
So, this equation is true for every value of $x$.
Thus, the given statement is true.