A is invertible and A^-1 = [2, 1; 3, 2]. What is A?

Question 56

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$A$ is invertible and $A^{-1} = \begin{bmatrix}2 & 1 \\ 3 & 2\end{bmatrix}$ . What is $A$ ?

\begin{bmatrix}2 & 1 \\ 3 & 2\end{bmatrix}

Correct answerYour answer

\begin{bmatrix}2 & -1 \\ -3 & 2\end{bmatrix}

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\begin{bmatrix}2 & -3 \\ -1 & 2\end{bmatrix}

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\begin{bmatrix}-2 & 1 \\ 3 & -2\end{bmatrix}

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CorrectNot quiteAnswer B

Correct answer: B

$A$ is the inverse of $A^{-1}$ : $(A^{-1})^{-1} = A$ .
$|A^{-1}| = 4 - 3 = 1$ , so $A = \operatorname{adj}(A^{-1}) = \begin{bmatrix}2 & -1 \\ -3 & 2\end{bmatrix}$ .

Worth noting

$\begin{bmatrix}2 & -3 \\ -1 & 2\end{bmatrix}$ is the transpose of the answer; check that its product with $A^{-1}$ is not $I$ .

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