How do you find the inverse of #A=##((5, 0), (1, 2))#?

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Answer 1 · 2016-05-06T19:24:41

#A^-1# = #((0.2, 0), (-0.1, 0.5))#

#A=##((5, 0), (1, 2))# compare with #A = ##((a, b),(c, d))#

First you need to find the determinant : 5x2 - 1x0 = 10

Now re-arrange the matrix: swop #a and d#

#A=##((2, 0), (1, 5))#

Change the signs of #b and c#

#A=##((2, 0), (-1, 5))#

Divide by the determinant

#A^(-1)=1/10##((2, 0), (-1, 5))# = #((0.2, 0), (-0.1, 0.5))#