Which of the following are the properties of matrices :-

AB \neq BA

in general

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The product of two non zero matrix may also be a zero matrix.

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A I = I A = A (where, I = identity matrix)

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AB = BA

always

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Solution

The correct options are
A $AB \neq BA$ in general
B The product of two non zero matrix may also be a zero matrix.
C $A I = I A = A (where, I = identity matrix)$
$\to In general, AB \neq BA as multiplication in matrices is not commutative .$
$\to The product of two non zero matrices may also be a zero matrix - (\begin{matrix} 0 & 1 0 & 1 \end{matrix}] \times (\begin{matrix} 2 & 0 0 & 0 \end{matrix}] = (\begin{matrix} 0 & 0 0 & 0 \end{matrix}] \to A I = (\begin{matrix} 2 & 0 0 & 0 \end{matrix}] \times (\begin{matrix} 1 & 0 0 & 1 \end{matrix}] = (\begin{matrix} 2 & 0 0 & 0 \end{matrix}] = A = (\begin{matrix} 1 & 0 0 & 1 \end{matrix}] \times (\begin{matrix} 2 & 0 0 & 0 \end{matrix}] = I A$

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