Questions on Algebra: Matrices, determinant, Cramer rule answered by real tutors!

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Question 162532: Find matrix X:

4. [3 4] [-3 -2] * X = [10 -10] [-8 8]
I have no clue where to even begin with this, I apperciate any help you have to offer me, id love to see the steps and correct answer. Thank you so much!: Find matrix X:

4. [3 4] [-3 -2] * X = [10 -10] [-8 8]
I have no clue where to even begin with this, I apperciate any help you have to offer me, id love to see the steps and correct answer. Thank you so much!
Answer by Fombitz(1789) About Me  (Show Source):
You can put this solution on YOUR website!

(matrix(2,2,3,4,-3,-2))(matrix(2,2,x[1],x[2],x[3],x[4]))=(matrix(2,2,10,-10,-8,8))
First find the inverse of your first matrix, which we'll call [A].
[A]=(matrix(2,2,3,4,-3,-2))
and the inverse of A called [A]inv.
[A]inv=(1/6)*(matrix(2,2,-2,-4,3,3))
and then matrix multiply both sides to solve for [X].
.
.
.
The problem would then look like this,
[A][X]=[B]
[A]inv[A][X]=[A]inv[B]
[I][X]=[A]inv[B]
[X]=[A]inv[B]
.
.
.
So we do the matrix multiplication,
[X]=(1/6)*(matrix(2,2,-2,-4,3,3))*(matrix(2,2,10,-10,-8,8))
[X]=(matrix(2,2,2,-2,1,-1))