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NDA 2012
Exam
NDA
Year
2012
Subject
Mathematics
Chapter
Matrices

NDA 2012 · Mathematics · Matrices

If the matrix AB is a zero matrix, then which one of the following...

If the matrix AB is a zero matrix, then which one of the following is correct?

Options

  1. AA must be equal to zero matrix or B must be equal to zero matrix
  2. BA must be equal to zero matrix and B must be equal to zero matrix
  3. CIt is not necessary that either A is zero matrix or B is zero matrix
  4. DNone of the above

Correct answer

C. It is not necessary that either A is zero matrix or B is zero matrix

Step-by-step solution

If A=\left[2000\begin{array}{ll}2 & 0 \\ 0 & 0\end{array}\right], B=\left[0020\begin{array}{ll}0 & 0 \\ 2 & 0\end{array}\right] then, A B=\left[0000\begin{array}{ll}0 & 0 \\ 0 & 0\end{array}\right] Here A≠0,B≠0\mathrm{A} \neq 0, \mathrm{ B} \neq 0 but AB=0\mathrm{AB}=0.
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