Which of the following is the inverse of matrix A?

Question 101

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Which of the following is the inverse of $A = \begin{bmatrix}3 & 5 \\ 1 & 2\end{bmatrix}$ ?

\begin{bmatrix}-2 & 5 \\ 1 & -3\end{bmatrix}

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\begin{bmatrix}3 & -5 \\ -1 & 2\end{bmatrix}

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\begin{bmatrix}2 & -1 \\ -5 & 3\end{bmatrix}

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\begin{bmatrix}2 & -5 \\ -1 & 3\end{bmatrix}

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CorrectNot quiteAnswer D

Correct answer: D

Multiply $A$ by the candidate: $\begin{bmatrix}3 & 5 \\ 1 & 2\end{bmatrix}\begin{bmatrix}2 & -5 \\ -1 & 3\end{bmatrix} = \begin{bmatrix}1 & 0 \\ 0 & 1\end{bmatrix}$ .
The product in the other order is $I$ as well, so this matrix is $A^{-1}$ .

Worth noting

$\begin{bmatrix}2 & -1 \\ -5 & 3\end{bmatrix}$ is the transpose of the inverse; it gives $\begin{bmatrix}-19 & 12 \\ -8 & 5\end{bmatrix}$ when multiplied by $A$ .

Concept: The inverse of a matrix
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The rule this testsInvertible matrices

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Ten questions from Matrices, at your own pace.

Which of the following is the inverse of A=[3512]A = \begin{bmatrix}3 & 5 \\ 1 & 2\end{bmatrix}A=[31​52​]?

Explanation

Which of the following is the inverse of $A = \begin{bmatrix}3 & 5 \\ 1 & 2\end{bmatrix}$ ?