Question

If A and B are matrices and AB = I, which of the following represents the value of B?

Answer 1

If the product of 2 matrices are I this means that B is inverse matrix of A.
the matrix A has been given 
if we put symbols for the numbers in matrix A as shown below;
$\left[\begin{array}{ccc}a&b\\c&d\\\end{array}\right]$
we need to first find the determinant (D)
D = ad - bc
where a = -1 , b = 4, c = -3 and d = 8
substituting these values 
D = -1x8 - (4x-3)
   = -8 +  12 = 4 
to find the inverse we need to exchange a and d and then multiply both b and c by -1
$\left[\begin{array}{ccc}8&-4\\3&-1\\\end{array}\right]$
and then have to divide all the terms in matrix by determinant (4)
$\left[\begin{array}{ccc} \frac{8}{4} & \frac{-4}{4} \\ \frac{3}{4} & \frac{-1}{4} \\\end{array}\right]$
the simplified inverse matrix B is;
$\left[\begin{array}{ccc} 2 & -1 \\ \frac{3}{4} & \frac{-1}{4} \\\end{array}\right]$

Answer 2

Answer:

4th option D

Step-by-step explanation: