CBSEJEEClass 12
How do you find the inverse of a matrix?
Answer
The inverse of a square matrix A is found using A⁻¹ = adj(A)/|A|, provided its determinant |A| is not zero.
The working
Check invertibility
First find the determinant |A|. The inverse exists only if |A| ≠ 0; such a matrix is called non-singular.
Find the cofactors
Compute the cofactor of each element of A to build the cofactor matrix.
Form the adjoint
Take the transpose of the cofactor matrix to get the adjoint, adj(A).
Apply the formula
Divide the adjoint by the determinant: A⁻¹ = adj(A)/|A|. Verify by checking that A·A⁻¹ = I.
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