# Answer to Question #21504 in Algebra for lishan hailu

Question #21504

the inverse of the matrix A=(1 1)

(3 2) is.........

(3 2) is.........

Expert's answer

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).

(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).

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