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# Given that find ​

-1
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Given that $$\begin{vmatrix} a & b & c \\ d & e & f \\ g & h & i \end{vmatrix} = -24,$$ find $$\begin{vmatrix} a & d & g \\ b & e & h \\ c & f & i \end{vmatrix}$$

May 14, 2022

#1
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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.

May 14, 2022
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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 $$\det(A^{\top})$$