Q175 / 270 · NDA 2012 (Phase 2) · Mathematics

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

  • A
    A must be equal to zero matrix or B must be equal to zero matrix
  • B
    A must be equal to zero matrix and B must be equal to zero matrix
  • Correct answer
    C
    It is not necessary that either A is zero matrix or B is zero matrix
  • D
    None of the above

Solution

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

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

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