Answer
The inverse is $ A=\left[ \begin{matrix}
0.6 & 0 & -0.4 & 0.2 \\
0.2 & 0 & 0.2 & -0.1 \\
0 & 1 & 0 & 0 \\
-1.2 & 0 & 0.8 & 0.1 \\
\end{matrix} \right]$.
Work Step by Step
Consider the given matrix, $ A=\left[ \begin{matrix}
1 & 2 & 0 & 0 \\
0 & 0 & 1 & 0 \\
1 & 3 & 0 & 1 \\
4 & 0 & 0 & 2 \\
\end{matrix} \right]$
We have to find the inverse of matrix $ A $ by using a calculator. We will follow the steps given below:
(1) We select the matrix $ A $ from the matrix edit menu and then enter or accept the dimensions.
(2) Use ${{2}^{nd}}$ and press the matrix button.
(3) Select the matrix $ A $ and use the function ${{X}^{-1}}$ for the inverse of matrix $ A $ and press enter.
(4) We find the ${{A}^{-1}}$
Therefore, the inverse of the matrix $ A $ is, $\left[ \begin{matrix}
.6 & 0 & -.4 & .2 \\
.2 & 0 & .2 & -.1 \\
0 & 1 & 0 & 0 \\
-1.2 & 0 & .8 & .1 \\
\end{matrix} \right]$
Now, check the result to show that $ A{{A}^{-1}}=I $. We multiply matrix $ A $ with ${{A}^{-1}}$ to obtain the identity matrix. Hence, the inverse of the given matrix is correct.
