SOLUTION: Find the inverse of A= (matrix) -3....1 -5....5 if it exists.

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Question 174766This question is from textbook Saxon Algebra 2
: Find the inverse of
A= (matrix) -3....1
-5....5
if it exists. This question is from textbook Saxon Algebra 2

Answer by KnightOwlTutor(293) About Me  (Show Source):
You can put this solution on YOUR website!
We know that the matrix has an inverse because the determinant is not equal to zero
[-3 1]
[-5 5]
[a b]
[c d]
To calculate the determinant ad-bc in this case -15+5=-10
Any Matrix inverse =1/ad-bc[d -b]
[-c a]
-1/10[5 -1]
[5 -3]
To double check multiply the matrices together and see if you come up with the identity matrix.
[-3 1]-1/10[5 -1]
[-5 5] [5 -3]
-15+5 3+3 -1/10[-10 0]
-25+25 5-15 -1/10[0 -10]

[1 0]
[0 1] is the identity matrix