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Mathematics Question on Inverse of a Matrix

The inverse of the matrix [200 030 004]\begin{bmatrix} 2 & 0 & 0 \\\ 0 & 3 & 0 \\\ 0 & 0 & 4 \end{bmatrix} is

A

[1200 0130 0014]\begin{bmatrix} \frac{1}{2} & 0 & 0 \\\ 0 & \frac{1}{3} & 0 \\\ 0 & 0 & \frac{1}{4} \end{bmatrix}

B

124[200 030 004]\frac{1}{24}\begin{bmatrix} 2 & 0 & 0 \\\ 0 & 3 & 0 \\\ 0 & 0 & 4 \end{bmatrix}

C

124[−200 0−30 00−4]\frac{1}{24}\begin{bmatrix} -2 & 0 & 0 \\\ 0 & -3 & 0 \\\ 0 & 0 & -4 \end{bmatrix}

D

[−1200 0−130 00−13]\begin{bmatrix} -\frac{1}{2} & 0 & 0 \\\ 0 & -\frac{1}{3} & 0 \\\ 0 & 0 & -\frac{1}{3} \end{bmatrix}

Answer

[1200 0130 0014]\begin{bmatrix} \frac{1}{2} & 0 & 0 \\\ 0 & \frac{1}{3} & 0 \\\ 0 & 0 & \frac{1}{4} \end{bmatrix}

Explanation

Solution

The correct option is (A) : [1200 0130 0014]\begin{bmatrix} \frac{1}{2} & 0 & 0 \\\ 0 & \frac{1}{3} & 0 \\\ 0 & 0 & \frac{1}{4} \end{bmatrix}.