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Mathematics · JEE | MATRICES

हिन्दी

What is the product \( AB \) if \( A = \begin{bmatrix} 0 & -1 \ 0 & 2 \end{bmatrix} \) and \( B = \begin{bmatrix} 3 & 5 \ 0 & 0 \end{bmatrix} \)?

  1. A
    \( \begin{bmatrix} 1 & 0 \ 0 & 1 \end{bmatrix} \)
  2. B
    \( \begin{bmatrix} 3 & 5 \ 0 & 2 \end{bmatrix} \)
  3. C
    \( \begin{bmatrix} 0 & 5 \ 0 & 0 \end{bmatrix} \)
  4. D
    \( \begin{bmatrix} 0 & 0 \ 0 & 0 \end{bmatrix} \)
View Answer & Solution

Correct answer · Option D

\( \begin{bmatrix} 0 & 0 \ 0 & 0 \end{bmatrix} \)

Explanation

Computing \( AB = \begin{bmatrix} 0 & -1 \ 0 & 2 \end{bmatrix} \begin{bmatrix} 3 & 5 \ 0 & 0 \end{bmatrix} = \begin{bmatrix} 0 & 0 \ 0 & 0 \end{bmatrix} \), showing two non-zero matrices can yield a zero matrix.
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