# Find the inverse of the following matrix A, if possible. Check that A*A^(-1) and A^(-1)*A=I A=[[4,8],[-5,-10]] The inverse, A^(-1), is A=?

Find the inverse of the following matrix A, if possible. Check that $A\ast {A}^{-1}$ and ${A}^{-1}\ast A=I$
$A=\left[\begin{array}{cc}4& 8\\ -5& -10\end{array}\right]$
The inverse, ${A}^{-1}$, is A=?
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Reese King
determinant matrix A = 4*-10 - 8*-5 = 0 => inconsistentmatrix => answer is not exist
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Ashlyn Krause
${A}^{-1}={\left[\begin{array}{cc}a& b\\ c& d\end{array}\right]}^{-1}=\frac{1}{ad-bc}\left[\begin{array}{cc}d& -b\\ -c& a\end{array}\right]$
$\frac{1}{-40-\left(-40\right)}=\frac{1}{0}$
Therefore there is no ${A}^{-1}$ so:
$\left[\begin{array}{cc}N& N\\ N& N\end{array}\right]$