Basic Maths - Grand Test 1 -Q10

+2 votes

Let A and B two matrices and matrix A has m rows and m-6 columns, matrix B has n rows and n^2 columns if AB = BA, then the value of n^2 is _____

asked Jun 21 in Basic Maths by gbeditor (21,290 points)
reshown Jun 23 by gbeditor

3 Answers

+2 votes
 
Best answer

\\ A_{m\times{(m-6)}} \and\ B_{n\times{n^2}}\\ \\AB\ is\ possible\ only\ when\ m-6=n \ \ \ \ \ \ \ \ \ \ (i)\\ \ BA \ is\ possible\ when\ n^2=m \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ (ii)\\ Squaring\ both\ sides\ in\ (i)\\ \\m^2-12m+36=n^2\\ m^2-12m+36=m \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ from (ii)\\ m^2-13m+36=0\\ m^2-9m-4m+36=0\\ m(m-9)-4(m-9)=0\\ (m-9)(m-4)=0\\ m=9 m=4\\ \\ Means\ n^2=9,4\\ \\ But\ value\ 4\ is\ not\ possible\ as\ A_{4\times{(-2)}}\ not\ possible

Therefore ans should be 9

answered Jun 23 by tskushagra-guptacse (11,660 points)
selected Jun 24 by gbeditor
for * u can use \times
+1 vote

9 is the correct answer.

answered Jun 23 by tsnikhilsharmagate2018 (24,690 points)
0 votes
question is wrong because after solving we are two matrix of order 3*9 and 9*3

so order of AB=3*3

and order of BA=9*9

and these matrices are not comparable because no.of rows and columns are different in both matrix
answered Jun 23 by tskaran25gupta (820 points)
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