Basic Maths - Grand Test 1 -Q10

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 _____

reshown Jun 23

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

Therefore ans should be 9

answered Jun 23 by (10,800 points)
selected Jun 24 by gbeditor
for * u can use \times
+1 vote