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
B
12
C
10
D
4

Solution

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

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