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Learn how to calculate the inverse of a 2x2 matrix with a formula. Get a complete understanding of the relationship between a matrix and its inverse. With five worked examples, you’ll master this skill in no time.
The inverse of 2x2 matrix A is a matrix A⁻¹ such that AA⁻¹ = A⁻¹A = I, where I is the identity matrix of order 2x2. Learn more about the inverse of a 2x2 matrix along with its formula, steps, and examples.
For an invertible matrix of order 2 x2, we can find the inverse in two different methods such as: Inverse using Elementary operations; Using the Inverse matrix formula; In the next section, you will go through the examples on finding the inverse of given 2×2 matrices. Inverse of a 2×2 Matrix Using Elementary Row Operations
To find the inverse of a 2×2 matrix, A, using row operations, first write the matrix as A=IA, where I is the identity matrix. Then apply a sequence of row operations to obtain the form I=BA, where B is the inverse matrix.
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Free online Inverse Matrix Calculator computes the inverse of a 2x2, 3x3 or higher-order square matrix. Also, eigenvalues, diagonalization, other properties of matrices.
The formula for the inverse of a $ 2 \times 2 $ matrix (Matrix $ A $) is given as: $ A^{ – 1 } = \frac{ 1 }{ad – bc} \begin{bmatrix} d & { – b } \\ { – c } & a \end {bmatrix} $ The quantity $ ad – bc $ is known as the determinant of the matrix.
