The following formula is used to calculate the inverse matrix value of the original 2×2 matrix:
\[ A^{-1} = \frac{1}{ad - bc} \begin{bmatrix} d & -b \\ -c & a \end{bmatrix} \]
Where:
An inverse matrix is the reciprocal of a given matrix of a fixed number of rows and columns. The inverse of a matrix \(A\) is denoted as \(A^{-1}\), and it is a matrix such that when multiplied by \(A\), it results in the identity matrix. The identity matrix is a matrix with ones on the diagonal and zeros elsewhere.
Let's assume the following values for the matrix:
First, calculate the determinant:
\[ \text{det} = (4 * 6) - (7 * 2) = 24 - 14 = 10 \]
Next, use the formula to find the inverse matrix:
\[ A^{-1} = \frac{1}{10} \begin{bmatrix} 6 & -7 \\ -2 & 4 \end{bmatrix} = \begin{bmatrix} 0.6 & -0.7 \\ -0.2 & 0.4 \end{bmatrix} \]
So, the inverse matrix is:
[\(0.6, -0.7\)]
[\(-0.2, 0.4\)]
