If the product of two matrices is a zero matrix, then:

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Solution

Q.
If the product of two matrices is a zero matrix, then:

1 at least one of the matrix is a zero matrix

2 both the matrices are zero matrices

3 it is not necessary that one of the matrices is a zero matrix

4 None of the above

Ans.
(3)

Ans. it is not necessary that one of the matrices is a zero matrix

Explanation:

Let $A = [\begin{matrix} 0 & - 1 \\ 0 & 2 \end{matrix}]$ and $B = [\begin{matrix} 3 & 5 \\ 0 & 0 \end{matrix}]$

Then, $A B = 0$ but $A$ and $B$ are non-zero.

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