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take terms and  and switch their positions. This is simply switching the elements on the main diagonal 
 
take terms and  and change those numbers to their opposites keeping there positions.


:now we find the determinant of this matrix
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product of the main diagonal-product of the other diagonal
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we take that result and divide every element in the matrix and the result is our inverse matrix
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the way you can check is to multiply the two together and see if your result is the identity matrix....if it is you can rest easy you have the correct answer.
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2)and 3)
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now I will let you do the steps to 2 and 3
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answers to 2 is 
...........3 is no solution as the determinant = 0
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4)X or=
3a+4b=6
2a+3b=5
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3R2-2R1(Row 2)---->R1-4R2(row 1)---->1/3R1---> so we end with 
a=-2
b=3
so X=
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5) is done the same as 4 but this time you have 3 variables....have fun