Assess whether the subsequent statement is always true or false, under the following conditions:

• The statement must be universally true for all possible values of the matrices and vectors. It should not be assumed true only in certain cases.
• Presumptions about the dimensions of matrices or vectors should be avoided unless specified, but they should be suitable for all operations like addition and multiplication in the statement.

Example: Declaring that A equals A is incorrect, as not all square matrices satisfy this condition.

1. If for every vector x, the norm of Ax is equal to the norm of Bx, it implies that matrices A = B.
2. For all vectors x, if \( x^{T}Ax \) = \( x^{T}Bx \), then this indicates that A equals B.
3. Matrix A must be the same as matrix B if, for any pair of vectors x and y, the expression\( x^{T}Ay \) is always equal to \( x^{T}By \).