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jok3333 [9.3K]
3 years ago
5

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

Mathematics
2 answers:
Ratling [72]3 years ago
6 0
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]

Stels [109]3 years ago
5 0

Answer:

4th option D

Step-by-step explanation:

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