# Find the inverse of matrices begin{bmatrix}8 & 6 5 & 4end{bmatrix}

Find the inverse of matrices
$\left[\begin{array}{cc}8& 6\\ 5& 4\end{array}\right]$
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Nathaniel Kramer
Step 1
here given matrix
$A=\left[\begin{array}{cc}8& 6\\ 5& 4\end{array}\right]$
Use the formula for $2×2$ matrices, which states
if $A=\left[\begin{array}{cc}a& b\\ c& d\end{array}\right]$
Thus ${A}^{-1}=\frac{1}{ad-bc}\left[\begin{array}{cc}d& -b\\ -c& a\end{array}\right]$
Step 2
Thus
${A}^{-1}=\frac{1}{2}\left[\begin{array}{cc}4& -6\\ -5& 8\end{array}\right]$
$=\left[\begin{array}{cc}2& -3\\ \frac{-5}{2}& 4\end{array}\right]$
Jeffrey Jordon