Question

The inverse of the matrix $A =\begin{bmatrix} {2}&{0} &{0}\\ {0}&{3}& {0} \\ {0}&{0}&{4}\\ \end{bmatrix}$ is

• A. $\begin{bmatrix} {2}&{0} &{0}\\ {0}&{3}& {0} \\ {0}&{0}&{4}\\ \end{bmatrix}$
• B. $\begin{bmatrix} {\frac {1}{2}}&{0} &{0}\\ {0}&{\frac {1}{3}}& {0} \\ {0}&{0}&{\frac {1}{4}}\\ \end{bmatrix}$
• C. $ \frac {1}{24}\begin{bmatrix} {2}&{0} &{0}\\ {0}&{3}& {0} \\ {0}&{0}&{4}\\ \end{bmatrix}$
• D. $\frac{1}{24}\left[\begin{array}{lll}1 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & 1\end{array}\right]$

Answer 1

Answer: (B)

The inverse of a diagonal matrix is obtained by replacing each element in the diagonal with its reciprocal. Hence the answer here would be:
$ A ^{-1}=\left[\begin{array}{ccc} \frac{1}{2} & 0 & 0 \\ 0 & \frac{1}{3} & 0 \\ 0 & 0 & \frac{1}{4} \end{array}\right] $