SOLUTION: find inverse of the matrix and also verify your result. 1 -2 3 4

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Question 175039: find inverse of the matrix and also verify your result.
1 -2
3 4
Answer by Mathtut(3670) About Me  (Show Source):
You can put this solution on YOUR website!

A=%28matrix%282%2C2%2C1%2C-2%2C3%2C4%29%29
A%5E-1=adjA%2FdetA
:
adjA=%28matrix%282%2C2%2C4%2C2%2C-3%2C1%29%29 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%5E-1=%28matrix%282%2C2%2C4%2C2%2C-3%2C1%29%29/10=%28matrix%282%2C2%2C2%2F5%2C1%2F5%2C-3%2F10%2C1%2F10%29%29
:
%28matrix%282%2C2%2C1%2C-2%2C3%2C4%29%29%28matrix%282%2C2%2C2%2F5%2C1%2F5%2C-3%2F10%2C1%2F10%29%29=%28matrix%282%2C2%2C1%2C0%2C0%2C1%29%29