Bonpoc: vert } a&b b&a vert 1) (a+b)^2 3) a^2+b^2 2) (a-b)^2 4) (a-b)(a+b) Packp oure onpenenutenb Tun omeema Bbl60poM OAHOrO BapuaHTOB

To solve the given problem, we need to find the determinant of the matrix:<br /><br />$\vert \begin{matrix} a&b\\ b&a\end{matrix} \vert$<br /><br />The determinant of a 2x2 matrix $\vert \begin{matrix} a&b\\ c&d\end{matrix} \vert$ is calculated as $ad - bc$.<br /><br />In this case, $a = a$, $b = b$, $c = b$, and $d = a$. So, the determinant is $a \cdot a - b \cdot b = a^2 - b^2$.<br /><br />Now, let's compare this result with the given options:<br /><br />1) $(a+b)^{2} = a^2 + 2ab + b^2$<br />2) $(a-b)^{2} = a^2 - 2ab + b^2$<br />3) $a^{2}+b^{2}$<br />4) $(a-b)(a+b) = a^2 - b^2$<br /><br />The correct answer is option 4) $(a-b)(a+b) = a^2 - b^2$, which matches our calculated determinant.