# Show that B is the multiplicative inverse of A, where: A=begin{bmatrix}2 & 1 1 & 1 end{bmatrix} text{ and } B=begin{bmatrix}1 & -1 -1 & 2 end{bmatrix}

Show that B is the multiplicative inverse of A, where:
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Arham Warner

Step 1
Here given matrices

Step 2
If B is the multiplicative inverse of A, then
$AB=I\left(identity\right)$
Now find
$A\cdot B=\left[\begin{array}{cc}2& 1\\ 1& 1\end{array}\right]\cdot \left[\begin{array}{cc}1& -1\\ -1& 2\end{array}\right]=\left[\begin{array}{cc}2-1& -2+2\\ 1-1& -1+2\end{array}\right]=\left[\begin{array}{cc}1& 0\\ 0& 1\end{array}\right]=I$
Therefore
B is the multiplicative inverse of A.

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Jeffrey Jordon

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