Question

Let  be two matrices such that they are commutative and , then the value of  is __​

Answer 1

Given :      $A=\left[\begin{array}{cc}1&2\\3&4\end{array}\right]$      and   $B=\left[\begin{array}{cc}a&b\\c&d\end{array}\right]$   are two matrices such that they are commutative with respect to multiplication and c ≠ 3b

To Find : Value of  (a-d)/(3b - c)

Solution:

$AB=\left[\begin{array}{cc}1&2\\3&4\end{array}\right] \left[\begin{array}{cc}a&b\\c&d\end{array}\right] = \left[\begin{array}{cc}a+2c&b+2d\\3a+4c&3b+4d\end{array}\right]$

$BA=\left[\begin{array}{cc}a&b\\c&d\end{array}\right] \left[\begin{array}{cc}1&2\\3&4\end{array}\right] = \left[\begin{array}{cc}a+3b&2a+4b\\c+3d&2c+4d\end{array}\right]$

AB = BA

=> a + 2c  = a + 3b  => 2c  = 3b

b + 2d = 2a + 4b  =>  2d = 2a + 3b

3a + 4c = c + 3d  =>  d  = a  + c   => a  - d = - c

(a -  d) /(3b - c)     =  (-c)/(2c - c)  = - 1

(a -  d) /(3b - c)     = - 1

Learn More:

If a and b are matrix with 32 and 56 elements respectively, then the ...

https://brainly.in/question/7583245

(First express metric measures in decimalnotation and then add.)(i)

https://brainly.in/question/12321830