For the matrix $A = \begin{bmatrix} 2 & 0 & 0 \ 0 & 3 & 0 \ 0 & 0 & …

Question

For the matrix $A = \begin{bmatrix} 2 & 0 & 0 \ 0 & 3 & 0 \ 0 & 0 & 4 \end{bmatrix}$, the inverse $A^{-1}$ is:

Accepted Answer

A. $\begin{bmatrix} 1/2 & 0 & 0 \ 0 & 1/3 & 0 \ 0 & 0 & 1/4 \end{bmatrix}$

For a diagonal matrix $A = \operatorname{diag}(a, b, c)$ with all entries non-zero, $A^{-1} = \operatorname{diag}(1/a, 1/b, 1/c)$. Check: $A \cdot A^{-1} = \operatorname{diag}(a/a, b/b, c/c) = I$.

Answer

$\begin{bmatrix} -2 & 0 & 0 \ 0 & -3 & 0 \ 0 & 0 & -4 \end{bmatrix}$

Answer

$\begin{bmatrix} 2 & 0 & 0 \ 0 & 3 & 0 \ 0 & 0 & 4 \end{bmatrix}$

Answer

The inverse does not exist

For the matrix $A = \begin{bmatrix} 2 & 0 & 0 \\ 0 & 3 & 0 \\ 0 & 0 & 4 \end{bmatrix}$, the inverse $A^{-1}$ is: