But it’s worth a review. Examples of Inverse Matrix in Excel; Introduction to Inverse Matrix in Excel. Related Topics: Matrices, Determinant of a 2×2 Matrix, Inverse of a 3×3 Matrix. By inverse matrix definition in math, we can only find inverses in square matrices. A matrix for which you want to compute the inverse needs to be a square matrix. Now we just have to take this determinant, multiply this times 1 over the determinant and we're there. Then we swap the positions of the elements in the leading diagonal and put a negative sign in front of the elements on the other diagonal. Finally multiply 1/deteminant by adjoint to get inverse. First, let us set up the matrices (be careful to get the rows and columns correct! We can find the inverse of only those matrices which are square and whose determinant is non-zero. Find the Inverse Matrix Using the Cayley-Hamilton Theorem Find the inverse matrix of the matrix $A=\begin{bmatrix} 1 & 1 & 2 \\ 9 &2 &0 \\ 5 & 0 & 3 \end{bmatrix}$ using the Cayley–Hamilton theorem. This step has the most calculations. Calculate the inverse of the matrix. 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