Question

Which pair of matrices are inverses of each another?

Answer 1

The last one, or (D). Just got it correct :)

Answer 2

if we put symbols for the numbers in the first matrix

`\left[\begin{array}{ccc}a&b\\c&d\\\end{array}\right]`
to find the inverse of the first matrix
first we need to find the determinant (D)
D = ad - bc
a = 2, b = 3 , c = 6 and d = 8
D = 2x8 - 3x6
= 16 - 18
= -2
then to find the inverse we have to exchange a and d and also multiply b and c by -1
and divide all the terms in the matrix by determinant
inverse matrix is then

`\left[\begin{array}{ccc} (8)/(-2) & (-3)/(-2) \\ (-6)/(-2) & (2)/(-2) \\\end{array}\right]`
simplified matrix, the answer of inverse matrix is

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