Find the inverse of A. Show all work. To find the inverse of A, solve the matrix equation AX = I for X

Question

A= [ 1 4 ]

[ -1 -3 ]

Answer 1

--------------------------

1 4 | 1 0

-1 -3 | 0 1

-------------------------

Adds row 1 + row 1:

--------------------------

1 4 | 1 0

0 1 | 1 1

-------------------------

-4 * row2 + row 1

--------------------------

1 0 | -3 -4

0 1 | 1 1

-------------------------

So the inverse is

-3 -4

1 1

check:

multiplies the matrices:

1 4 -3 -4

-1 -3 1 1

and

-3 -4 1 4

1 1 -1 -3

both result in the identity matrix, so the inverse is correct

So the inverse is

-3 -4

1 1