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### What is Adjoint and Inverse of Matrix?

The adjoint of a square matrix A is the transpose of the matrix of cofactors of A, denoted as adj(A). It can be used to find the inverse of a matrix, if it exists.

The inverse of a matrix A, denoted as A^-1, is a matrix that satisfies the equation A * A^-1 = I, where I is the identity matrix. If a matrix has an inverse, it is called invertible. Not all matrices have an inverse.

The formula for finding the inverse of a 2×2 matrix is:

A^-1 = (1/det(A)) * [[d, -b], [-c, a]]

where, det(A) is the determinant of A and a, b, c, and d are the entries of the original matrix.

For matrices of larger sizes, the adjoint and inverse can be found using advanced linear algebra methods such as Gaussian elimination or LU decomposition.