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Answer whether the following statements are True or False.

There exists $A=\left(\begin{array}{ll}a & b \\ c & d\end{array}\right) \in \mathrm{M}_{2}(\mathbb{R})$, with $A^{2}=A \neq 0$, such that

$$|a|+|b|<1 \quad \text{and} \quad|c|+|d|<1.$$

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