Determinant of a compound expression

MediumLinear Algebra~3m

Let $A$ and $B$ be $3\times3$ matrices with $\det(A)=3$ and $\det(B)=2$ . Compute $\det\!\big(A^{2}\,B^{-1}\,A^{\top}\big)$ . Give a decimal to two places.

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Push $\det$ through: $\det(XY)=\det X\det Y$ , $\det(X^{-1})=1/\det X$ , $\det(X^{\top})=\det X$ .
$\det(A^2)=9$ , $\det(B^{-1})=1/2$ , $\det(A^{\top})=3$ .

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13.5 (± 0.001)

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Determinant of a compound expression

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