Question 982106
let A be the given matrix, then if A inverse ( A(-1) ) exists then
A x A(-1) = A(-1) x A = I where I is the identity matrix
first we calculate A(-1)
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let A = 
a  b
c  d
then
A(-1) = (1 / (ad - bc)) x 
d -b
-c a
for the given matrix A =
1 1
2 3
A(-1) = (1 / (3-2)) x
3 -1
-2 1
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now check that A(-1) works
A x A(-1) =
1 1
2 3
x
3 -1
-2 1 =
3-2  1-1
6-6 -2+3 =
1 0
0 1
therefore we have
A x A(-1) = I
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now check
A(-1) x A =
3 -1
-2 1 x
1 1
2 3 =
3-2  3-3
-2+2 -2+3 =
1 0
0 1
therefore we have
A(-1) x A = I
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A(-1) exists and A(-1) =
3 -1
-2 1