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evaluate the following determinants:
matrix of [ad+bc bd-ac
ac-bd ad+bc]

Dear Student,

|\begin{matrix} ad + bc & bd - ac \\ ac - bd & ad + bc \end{matrix}| = |\begin{matrix} ad & bd \\ ac & ad \end{matrix}| + |\begin{matrix} bc & - ac \\ - bd & bc \end{matrix}| = ad |\begin{matrix} d & b \\ c & a \end{matrix}| + bc |\begin{matrix} c & - a \\ - d & b \end{matrix}| = ad (ad - bc) + bc (bc - ad) = a^{2} d^{2} - abcd + b^{2} c^{2} - abcd = a^{2} d^{2} + b^{2} c^{2} - 2 abcd

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