Find the inverse of `A=[[1, 3 ,3] ,[1 ,4, 3], [1, 3, 4]]` and verify that `A^(-1)A=I_3dot`

Explanation

To find the inverse of the matrix \( A = \begin{bmatrix} 1 & 3 & 3 \\ 1 & 4 & 3 \\ 1 & 3 & 4 \end{bmatrix} \) and verify that \( A^{-1}A = I_3 \), we will follow these steps:

### Step 1: Calculate the Determinant of Matrix A
The determinant of a \( 3 \times 3 \) matrix \( A = \begin{bmatrix} a & b & c \\ d & e & f \\ g & h & i \end{bmatrix} \) is given by:
\[ \text{det}(A) = a(ei - fh) - b(di - fg) + c(dh - eg) \]

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