SOLUTION: find the inverse for the matrix, if it exists. If it does not exist, state that it does not exist. Please solve and show work. Thank you. 1 1 2 3

Question 982106: find the inverse for the matrix, if it exists. If it does not exist, state that it does not exist. Please solve and show work. Thank you.
1 1
2 3
Answer by rothauserc(4718) (Show Source): You can put this solution on YOUR website!
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)
******************************************************************
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
*************************************
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
***************************************
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
****************************************
A(-1) exists and A(-1) =
3 -1
-2 1

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