$$A = \begin{bmatrix} 1 & 2 & 7 \\ 1 & 3 & 4 \\ 2 & 5 & 8 \end{bmatrix}$$ Find the determinant of A. Let $B = [b_{ij}]$ be the inverse matrix of A, find $b_{23}$.
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$$det(A) = 1(3 \cdot 8 - 4 \cdot 5) - 2(1 \cdot 8 - 4 \cdot 2) + 7(1 \cdot 5 - 3 \cdot 2)$$ $$det(A) = 1(24 - 20) - 2(8 - 8) + 7(5 - 6)$$ $$det(A) = 1(4) - 2(0) + 7(-1)$$ $$det(A) = 4 - 0 - 7$$ $$det(A) = -3$$ Show more…
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