ConvertOnlineMatrix InverseCalculator
Matrix A size: x
Answer
How to use this Matrix Inverse Calculator 🤔
Follow these steps to perform Matrix Inverse for the given matrices.
- Enter the matrix size for matrix A.
- Based on the given matrix size, a matrix of input fields appears. Enter the matrix elements.
- As and when you complete entering the matrix elements, Matrix Inverse is calculated, and displayed in the answer section.
Matrix Inverse
The inverse of a matrix A is another matrix, denoted as A-1, such that when A is multiplied by A-1, the result is the identity matrix. The matrix A must be square (same number of rows and columns) and have a non-zero determinant to have an inverse.
The inverse of a matrix A is computed as:
\( A^{-1} = \frac{1}{\det(A)} \cdot \text{adj}(A) \)
where \( \det(A) \) is the determinant of A and \( \text{adj}(A) \) is the adjugate of A.
Example 1
Let's find the inverse of the following 2x2 matrix:
\( A = \begin{bmatrix} 1 & 2 \\ 3 & 4 \end{bmatrix} \)
The determinant of A is:
\( det(A) = (1 \times 4) - (2 \times 3) = 4 - 6 = -2 \)
The adjugate of A is:
\( \text{adj}(A) = \begin{bmatrix} 4 & -2 \\ -3 & 1 \end{bmatrix} \)
Therefore, the inverse of A is:
\( A^{-1} = \frac{1}{-2} \times \begin{bmatrix} 4 & -2 \\ -3 & 1 \end{bmatrix} = \begin{bmatrix} -2 & 1 \\ 1.5 & -0.5 \end{bmatrix} \)