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Question

Let A =  $$[m \, n] _1 \, _\times \,  _2$$ , B = $$\begin{bmatrix}m\\ n\end{bmatrix} \, _2 \, _\times \,_ 1$$ and C = $$[25] \, _1 \, _\times \,_1$$  be three matrices such that AB = C, where m and n are integers, then the number of ordered pairs of (m,n) are 


A
8
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B
12
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C
10
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D
4
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Solution

The correct option is C 12
$$m^2 \,+ \,  n^2 \, = \, 25$$ 
$$\therefore  \, (0 \, \pm  \, 5), \, \left ( \pm 5,0 \right ) \, \left ( \pm 3, \, \pm 4 \right ),\, \left ( \pm 4 ,\pm 3 \right )$$

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