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Inverse Matrix Calculator

Formula

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:

$A^{-1}$ is the inverse matrix
$a, b, c, d$ are the elements of the original matrix
$ad - bc$ is the determinant of the original matrix

What is an Inverse Matrix?

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.

Example Calculation

Let's assume the following values for the matrix:

$a = 4$
$b = 7$
$c = 2$
$d = 6$

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:

[ $0.6, -0.7$ ]

[ $-0.2, 0.4$ ]

Inverse Matrix Calculator

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Formula

What is an Inverse Matrix?

Example Calculation