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Matrices — Maths STD 12 Science — Question

Gujarat BoardEnglish MediumSTD 12 ScienceMathsMatrices1 Mark
MCQ
If the matrix $AB$ is zero, then :
  • ✓
    It is not necessary that either $A = 0$ or, $B = 0$
  • B
    $A = 0$ or $B = 0$
  • C
    $A = 0$ and $B = 0$
  • D
    All the above statements are wrong
✓

Answer

Correct option: A.
It is not necessary that either $A = 0$ or, $B = 0$
Let $\text{A}=\begin{bmatrix}0&2\\0&0\end{bmatrix}$ and $\text{B}=\begin{bmatrix}1&0\\0&0\end{bmatrix}$
$\therefore \text{AB}=\begin{bmatrix}0&2\\0&0\end{bmatrix}\begin{bmatrix}1&0\\0&0\end{bmatrix}=\begin{bmatrix}0&0\\0&0\end{bmatrix}$

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