Find AB, if A= [ ll 6 & 9 2 & 3 ] and B= [ lll 2 & 6 & 0 7 & 9 & … - Vidyadip

Question

Find AB, if $A=\left[\begin{array}{ll} {6} & {9} \\ {2} & {3} \end{array}\right] \text { and } B=\left[\begin{array}{lll} {2} & {6} & {0} \\ {7} & {9} & {8} \end{array}\right]$

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Answer

Matrix A has 2 columns which is equal to the number of rows of B. Hence AB is defined. Now
$A B=\left[\begin{array}{lll} {6(2)+9(7)} & {6(6)+9(9)} & {6(0)+9(8)} \\ {2(2)+3(7)} & {2(6)+3(9)} & {2(0)+3(8)} \end{array}\right]$
$=\left[\begin{array}{ccc} {12+63} & {36+81} & {0+72} \\ {4+21} & {12+27} & {0+24} \end{array}\right]$
$=\left[\begin{array}{ccc} {75} & {117} & {72} \\ {25} & {39} & {24} \end{array}\right]$

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