Answer to Question #21504 in Algebra for lishan hailu

Question

the inverse of the matrix A=(1 1)
(3 2) is.........

Answer 1

Let's find the inverse matrix A^(-1):

(1 1 | 1 0 )
(3 2 | 0 1 )

& ~

(1& 1 |& 1& 0 )
(0 -1 | -3& 1 )

& ~

(1& 0 | -2& 1 )
(0 -1 | -3& 1 )

& ~

(1& 0 | -2& 1 )
(0& 1 |& 3 -1 ).

Therefore,

A^(-1) = (-2& 1 )
( 3 -1 ).


Really,

(1 1)*(-2& 1) = (1 0)
(3 2) ( 3 -1) (0 1).