Find AB, if A = [ cc 0 & -1 0 & 2 ] and B= [ ll 3 & 5 0 & 0 ] - Vidyadip

Question

Find AB, if A = $\left[\begin{array}{cc} {0} & {-1} \\ {0} & {2} \end{array}\right] \text { and } B=\left[\begin{array}{ll} {3} & {5} \\ {0} & {0} \end{array}\right]$

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Answer

We have $A B=\left[\begin{array}{rr} {0} & {-1} \\ {0} & {2} \end{array}\right]\left[\begin{array}{ll} {3} & {5} \\ {0} & {0} \end{array}\right]=\left[\begin{array}{ll} {0} & {0} \\ {0} & {0} \end{array}\right]$
Thus, if the product of two matrices is a zero matrix, it is not necessary that one of the matrices is a zero matrix.

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