# Find the inverse of the following matrix A, if possible. Check that AA^(-1)=I and A^(-1)A=I A=[[7,4],[7,7]] The inverse, A^(-1) is?

Find the inverse of the following matrix A, if possible. Check that $A{A}^{-1}=I$ and ${A}^{-1}A=I$
$A=\left[\begin{array}{cc}7& 4\\ 7& 7\end{array}\right]$
The inverse, ${A}^{-1}$ is ?
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Izabelle Frost
$\frac{1}{ab-bc}\left[\begin{array}{cc}d& -b\\ -c& a\end{array}\right]$
$\frac{1}{49-28}\left[\begin{array}{cc}7& -4\\ -7& 7\end{array}\right]$
$\left[\begin{array}{cc}1/3& -4/21\\ -1/3& 1/3\end{array}\right]$
###### Not exactly what you’re looking for?
Elisabeth Esparza
.
Inverse of a $2×2$ matrix:
If . If ad-bc=0, then A has no inverse.
So, ${A}^{-1}=\frac{1}{7\ast 7-4\ast 7}\left[\begin{array}{cc}7& -4\\ -7& 7\end{array}\right]=\frac{1}{21}\left[\begin{array}{cc}7& -4\\ -7& 7\end{array}\right]=\left[\begin{array}{cc}\frac{7}{21}& -\frac{4}{21}\\ -\frac{7}{21}& \frac{7}{21}\end{array}\right]=\left[\begin{array}{cc}\frac{1}{3}& -\frac{4}{21}\\ -\frac{1}{3}& \frac{1}{3}\end{array}\right]$