Question 175039
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A={{{(matrix(2,2,1,-2,3,4))}}}

{{{A^-1=adjA/detA}}} 
:
adjA={{{(matrix(2,2,4,2,-3,1))}}} in a 2x2 matrix...the elements of the main diagonal of the matrix A are switched whereas we take the negatives of the remaining elements to obtain the adjugate of A 
:
detA=1(4)-2(-3)=10
:
{{{A^-1=(matrix(2,2,4,2,-3,1))}}}/10={{{(matrix(2,2,2/5,1/5,-3/10,1/10))}}}
:
{{{(matrix(2,2,1,-2,3,4))}}}{{{(matrix(2,2,2/5,1/5,-3/10,1/10))}}}={{{(matrix(2,2,1,0,0,1))}}}