Question

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

A= [-1, 4
-3, 8]

Answer 1

4th option D

Explanation:

Answer 2

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} (8)/(4) & (-4)/(4) \\ (3)/(4) & (-1)/(4) \\\end{array}\right]`
the simplified inverse matrix B is;

`\left[\begin{array}{ccc} 2 & -1 \\ (3)/(4) & (-1)/(4) \\\end{array}\right]`