Introduction
- Ever wondered what happens when you multiply a square matrix by its inverse? Let’s uncover this mathematical marvel step by step!
- Let us consider the Square Matrix A and the inverse A-1
\[\Large
A =
\begin{bmatrix}
1 & 2 & 3 \\
4 & 1 & 5 \\
6 & 0 & 2 \\
\end{bmatrix}
\]
\[\Large
A^{-1} =
\frac{1}{28}
\begin{bmatrix}
2 & 4 & 7 \\
-22 & 16 & 7 \\
6 & -12 & 7 \\
\end{bmatrix}
\]
\[\Large
A \cdot A^{-1} = \frac{1}{28}
\begin{bmatrix}
\textcolor{#007BFF}{1} & \textcolor{#007BFF}{2} & \textcolor{#007BFF}{3} \\
\textcolor{#007BFF}{4} & \textcolor{#007BFF}{1} & \textcolor{#007BFF}{5} \\
\textcolor{#007BFF}{6} & \textcolor{#007BFF}{0} & \textcolor{#007BFF}{2} \\
\end{bmatrix}
\begin{bmatrix}
\textcolor{#FF0000}{2} & \textcolor{#FF0000}{4} & \textcolor{#FF0000}{7} \\
\textcolor{#FF0000}{-22} & \textcolor{#FF0000}{16} & \textcolor{#FF0000}{7} \\
\textcolor{#FF0000}{6} & \textcolor{#FF0000}{-12} & \textcolor{#FF0000}{7} \\
\end{bmatrix}
\]
- Try the above multiplication and click next when you are ready to review your answer.
- Unsure of how to multiply check out the Matrix multiplication lesson.
What is the result of multiplying Matrix \( A \) by its inverse \( A^{-1} \)?