Given that \(\begin{vmatrix} a & b & c \\ d & e & f \\ g & h & i \end{vmatrix} = -24,\) find \(\begin{vmatrix} a & d & g \\ b & e & h \\ c & f & i \end{vmatrix}\)
Directly use the following property of determinants:
Suppose A is a square matrix. Then \(\det A = \det(A^{\top})\), where \(A^\top\) is the transpose of A.
I tried 24 but thats not it
Let \(A = \begin{pmatrix}a&b&c\\d&e&f\\g&h&i\end{pmatrix}\), you are given \(\det(A)\) = -24, and you are to find \(\det(A^{\top})\).
Combine this with the formula I stated. Is this clearer to you now?
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