Find the inverse of the matrix.
\begin{equation*}
A = \begin{bmatrix}
1 & -1 & 0\\
1 & 0 & -1\\
-6 & 2 & 3
\end{bmatrix}
\end{equation*}
Section 2.3 Inverse Matrix
Checkpoint 2.3.1.
How to find the inverse of a square matrix? that is, to find another matrix \(B\) such that
\begin{equation*}
AB=BA=I_n
\end{equation*}
Let \(B=[\beta_1\,\beta_2\,\ldots\, \beta_n]\) and \(I_n=[\mathbf{e}_1\ \mathbf{e}_2\ \ldots\ \mathbf{e}_n]\text{.}\) \(AB=I_n\) can be read as
\begin{equation*}
AB=A[\beta_1\,\beta_2\,\ldots\, \beta_n]=[A\beta_1\, A\beta_2\ ,\ldots, \ A\beta_n]=[\mathbf{e}_1,\mathbf{e}_2,\ldots, \mathbf{e}_n],
\end{equation*}
What is the nature of invertibility of a square matrix? You can think it is the generalization of nonzero numbers.
