Q45 / 160 · WBJEE 2010 · Mathematics

If the matrices $A=\left[\begin{array}{lll}2 & 1 & 3 \\ 4 & 1 & 0\end{array}\right]$ and $B=\left[\begin{array}{rr}1 & -1 \\ 0 & 2 \\ 5 & 0\end{array}\right]$, then $\mathrm{AB}$ will be

  • Correct answer
    A
    $\left[\begin{array}{cr}17 & 0 \\ 4 & -2\end{array}\right]$
  • B
    $\left[\begin{array}{ll}4 & 0 \\ 0 & 4\end{array}\right]$
  • C
    $\left[\begin{array}{cr}17 & 4 \\ 0 & -2\end{array}\right]$
  • D
    $\left[\begin{array}{ll}0 & 0 \\ 0 & 0\end{array}\right]$

Solution

$$ \text { Hints : } \mathrm{AB}=\left[\begin{array}{lll} 2 & 1 & 3 \\ 4 & 1 & 0 \end{array}\right]\left[\begin{array}{rr} 1 & -1 \\ 0 & 2 \\ 5 & 0 \end{array}\right]=\left[\begin{array}{lr} 17 & 0 \\ 4 & -2 \end{array}\right] $$

Hence, the correct answer is option: 'A'.

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