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Question:
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Consider the following statements:
$1.$ The product of two non-zero matrices can never be identity matrix.
$2.$ The product of two non-zero matrices can never be zeromatrix.
Which of the above statements is/are correct?
Options:
$1.$ The product of two non-zero matrices can never be identity matrix.
$2.$ The product of two non-zero matrices can never be zeromatrix.
Which of the above statements is/are correct?
Solution:
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Verified Answer
The correct answer is:
Neither lnor 2
If B $=\mathrm{A}^{-1}$, then $\mathrm{AB}=\mathrm{I}$ (identity matrix) Therefore, statement 1 is false.
$\mathrm{I}=\left[\begin{array}{ll}1 & 0 \\ 0 & 1\end{array}\right]$ and $\mathrm{A}=\left[\begin{array}{ll}0 & 2 \\ 2 & 0\end{array}\right]$, then $\mathrm{IA}=\left[\begin{array}{ll}1 & 0 \\ 0 & 1\end{array}\right]$
$\left[\begin{array}{ll}0 & 2 \\ 2 & 0\end{array}\right]=0$
Therefore, statement 2 is not correct.
$\mathrm{I}=\left[\begin{array}{ll}1 & 0 \\ 0 & 1\end{array}\right]$ and $\mathrm{A}=\left[\begin{array}{ll}0 & 2 \\ 2 & 0\end{array}\right]$, then $\mathrm{IA}=\left[\begin{array}{ll}1 & 0 \\ 0 & 1\end{array}\right]$
$\left[\begin{array}{ll}0 & 2 \\ 2 & 0\end{array}\right]=0$
Therefore, statement 2 is not correct.
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