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Mathematics Question on Matrices

If A=[1√30−√310 002]A= \begin{bmatrix}1&√3&0 \\\\-√3&1&0 \\\ 0&0&2 \end{bmatrix} and B=[√310−1√30 002]B=\begin{bmatrix}√3&1&0 \\\\-1&√3&0 \\\ 0&0&2 \end{bmatrix} then AB is equal to :

A

4I4I

B

−4I-4I

C

[004 040 −400]\begin{bmatrix} 0&0&4 \\\ 0&4&0 \\\ -4 &0 &0 \end{bmatrix}

D

[040 −400 004]\begin{bmatrix} 0&4&0\\\ -4&0&0 \\\ 0&0 &4 \end{bmatrix}

Answer

[040 −400 004]\begin{bmatrix} 0&4&0\\\ -4&0&0 \\\ 0&0 &4 \end{bmatrix}

Explanation

Solution

The correct option is(D):[040 −400 004]\begin{bmatrix} 0&4&0\\\ -4&0&0 \\\ 0&0 &4 \end{bmatrix}