SOLUTION: 1. If A= [2 -4] [-2 5] FIND A^-1 2. use the question & answer above to calculate A X A^-1

Question 389536: 1.
If A=
[2 -4]
[-2 5]
FIND A^-1
2.
use the question & answer above to calculate A X A^-1
Answer by haileytucki(390) (Show Source): You can put this solution on YOUR website!
M[2,-4:-2,5]
These are both valid notations for the determinant of a matrix.
detM[2,-4:-2,5]=M[D,2,-4:-2,5]
The determinant of a 2x2 matrix can be found using the formula M[D,a,b:c,d]=ad-cb
detM[2,-4:-2,5]=(2)(5)-(-2)(-4)
Simplify the determinant.
detM[2,-4:-2,5]=2
The determinant of M[2,-4:-2,5] is 2.
2
Now, just plug in the 2 to the next question;
2^(-1)
Remove the negative exponent by rewriting 2^(-1) as (1)/(2). A negative exponent follows the rule a^(-n)=(1)/(a^(n)).
(1)/(2)

And the last question:

2*2^(-1)
Remove the negative exponent by rewriting 2^(-1) as (1)/(2). A negative exponent follows the rule a^(-n)=(1)/(a^(n)).
2*(1)/(2)
Cancel the common factor of 2 from the first term 2 and the denominator of the second term (1)/(2).
1*1
Multiply 1 by 1 to get 1.
1

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