What is the inverse of matrix A?

Question 100

EasyOriginal question

What is the inverse of $A = \begin{bmatrix}2 & 0 \\ 0 & 5\end{bmatrix}$ ?

\begin{bmatrix}-2 & 0 \\ 0 & -5\end{bmatrix}

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\begin{bmatrix}5 & 0 \\ 0 & 2\end{bmatrix}

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\begin{bmatrix}\frac{1}{2} & 0 \\ 0 & \frac{1}{5}\end{bmatrix}

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\begin{bmatrix}\frac{1}{5} & 0 \\ 0 & \frac{1}{2}\end{bmatrix}

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CorrectNot quiteAnswer C

Correct answer: C

For a diagonal matrix with non-zero diagonal elements, the inverse takes the reciprocal of each.
$A^{-1} = \begin{bmatrix} \frac{1}{2} & 0 \\ 0 & \frac{1}{5} \end{bmatrix}$ ; check: $AA^{-1} = I$ .

Worth noting

Swapping the diagonal elements, as the 2 × 2 shortcut does, still needs dividing by the determinant, 10.

Ten questions from Matrices, at your own pace.