EXAMPLE FA/5 53 5 17 and B = 12 31 ...
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EXAMPLE FA/5 53 5 17 and B = 12 31 16 8 4 find AB and BA whichever exists.

11th - 12th Class
Maths
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Here, ( A ) is a ( 2 times 2 ) matrix and ( B ) is a ( 2 times 3 ) matrix. Clearly, the number of columns in ( A= ) number of rows in ( B ). ( therefore A B ) exists and it is a ( 2 times 3 ) matrix. [ begin{aligned} A B &=left[begin{array}{cc} 5 & 4 2 & 3 end{array}right]left[begin{array}{ccc} 3 & 5 & 1 6 & 8 & 4 end{array}right] &=left[begin{array}{ccccc} 5 cdot 3+4 cdot 6 & 5 cdot 5+4 cdot 8 & 5 cdot 1+4-4 & 2 cdot 3+3 cdot 6 & 2 cdot 5+3 cdot 8 & 2 cdot 1+3 cdot 4 end{array}right.& & &=left[begin{array}{ccc} 15+24 & 25+32 & 5+16 6+18 & 10+24 & 2+12 end{array}right]=left[begin{array}{ccc} 39 & 57 & 21 24 & 34 & 14 end{array}right] end{aligned} ] ( operatorname{Again}, B ) is a ( 2 times 3 ) matrix and ( A ) is a ( 2 times 2 ) matrix. ( therefore ) number of columns in ( B eq ) number of rows in ( A ) So, ( B A ) does not exist.
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