Inverse of 2×2 Matrix Example
Inverse of the 2×2 matrix can also be calculated using the shortcut method apart from the method discussed above. Let’s consider an example to understand the shortcut method to calculate the inverse of 2 × 2 Matrix.
For given matrix A = [Tex]\begin{bmatrix}a & b\\ c & d\end{bmatrix} [/Tex]
We know, |A| = (ad – bc)
and adj A = [Tex]\begin{bmatrix}d & -b\\ -c & a\end{bmatrix} [/Tex]
then using the formula for inverse
A-1 = (1 / |A|) × Adj A
⇒ A-1 = [Tex][1 / (ad – bc)] × \begin{bmatrix}d & -b\\ -c & a\end{bmatrix} [/Tex]
Thus, the inverse of the 2 × 2 matrix is calculated.
Inverse of 3X3 Matrix Example
Let us take any 3×3 Matrix A = [Tex]\begin{bmatrix}a & b & c\\ l & m & n\\ p & q & r\end{bmatrix} [/Tex]
The inverse of 3×3 matrix is calculated using the inverse matrix formula,
A-1 = (1 / |A|) × Adj A
Inverse of a Matrix
The inverse of Matrix is the matrix that on multiplying with the original matrix results in an identity matrix. For any matrix A, its inverse is denoted as A-1.
Let’s learn about the Matrix Inverse in detail, including its definition, formula, methods on how to find the inverse of a matrix, and examples.
Table of Content
- Matrix Inverse
- Terms Related to Matrix Inverse
- How to Find Inverse of Matrix?
- Inverse of a Matrix Formula
- Inverse Matrix Method
- Inverse of 2×2 Matrix Example
- Determinant of Inverse Matrix
- Properties of Inverse of Matrix
- Matrix Inverse Solved Examples