1. Problem: You asked 'On for matrix step by step'. Please provide the matrix entries and specify the operation you want (for example determinant, inverse, row reduction, or eigenvalues). 2. Example solution: inverse of a $2\times2$ matrix step by step. $$A = \begin{pmatrix} a & b \\ c & d \end{pmatrix}$$ 3. Compute the determinant. Compute $\det(A) = ad - bc$. 4. Check invertibility. The matrix is invertible iff $ad - bc \neq 0$. 5. Compute the adjugate matrix. $$\operatorname{adj}(A) = \begin{pmatrix} d & -b \\ -c & a \end{pmatrix}$$ 6. Form the inverse. $$A^{-1} = \frac{1}{ad - bc} \begin{pmatrix} d & -b \\ -c & a \end{pmatrix}$$ 7. Numerical example. $$A = \begin{pmatrix} 2 & 1 \\ 3 & 4 \end{pmatrix}$$ Compute $\det(A) = 2\cdot4 - 1\cdot3 = 5$. $$\operatorname{adj}(A) = \begin{pmatrix} 4 & -1 \\ -3 & 2 \end{pmatrix}$$ $$A^{-1} = \frac{1}{5} \begin{pmatrix} 4 & -1 \\ -3 & 2 \end{pmatrix} = \begin{pmatrix} 4/5 & -1/5 \\ -3/5 & 2/5 \end{pmatrix}$$ Final answer: The inverse is the matrix above.