# Select and write the most appropriate answer from the given alternatives in each of the following : The inverse of the matrix {:((1,-1),(2,3)):} is

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Select and write the most appropriate answer from the given alternatives in each of the following :
The inverse of the matrix {:((1,-1),(2,3)):} is
A. (1)/(5)[{:(3,-1),(-2,1):}]
B. (1)/(5)[{:(3,1),(-2,1):}]
C. (1)/(5)[{:(-3,1),(-2,1):}]
D. (1)/(5)[{:(3,-1),(2,-1):}]

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Let A = [{:(1,-1),(2,3):}]
|A| = 3-(-2) = 5
Cofactors of A, a_(11) = 3,a_(12) = - 2
a_(21) = 1,a_(22) = 1
So, matrix of cofactor = [{:(3,-2),(1,1):}]
A^(-1) =(1)/(|A|)adj A
 = (1)/(5)[{:(3,-2),(1,1):}]
A^(-1) = (1)/(5) [{:(3,1),(-2,1):}]
Hence, the corrct answer from the given alternativeis (b)