Two different non-zero operators $\widehat{\mathrm{A}}$ and $\widehat{\mathrm{B}}(\widehat{\mathrm{A}} \neq \widehat{\mathrm{B}})$ satisfy the relation $(\widehat{\mathrm{A}}+\widehat{\mathrm{B}})(\widehat{\mathrm{A}}-\widehat{\mathrm{B}})= \widehat{A}^{2}-\widehat{B}^{2}$
(a)$\widehat{A} \widehat{B}=\widehat{A}^{2}$ and $\widehat{B} \widehat{A}=\widehat{B}^{2}$