Question

Let A = $[mn{]}_1{}_{\times }{}_2$ , B = $\left[\begin{array}{c}m\\ n\end{array}\right]{}_2{}_{\times }{}_1$ and C = $\left[25\right]{}_1{}_{\times }{}_1$ 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

Answer 1

Answer: (B)

12

$m^2+n^2=25$
$\therefore (0\pm 5),(\pm 5,0)(\pm 3,\pm 4),(\pm 4,\pm 3)$