First slide

Operations of matrix

Question

If the matrix AB is zero, then

Moderate

A

It is not necessary that either A = O or, B = O
B

A =O or B=O
C

A =O and B =O
D

all the above statements are wrong

Solution

If $A = [\begin{array}{ll} 1 0 \\ 0 0 \end{array}], B = [\begin{array}{ll} 0 0 \\ 0 1 \end{array}],$ then $A B = [\begin{array}{ll} 0 0 \\ 0 0 \end{array}]$
However, $A \neq O, B \neq O$
So, option (a) is correct

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