The inverse of a matrix is just a reciprocal of the matrix as we do in normal arithmetic for a single number which is used to solve the equations to find the value of unknown variables. The inverse of a matrix is that matrix which when multiplied with the original matrix will give as an identity matrix.

Finding the inverse of a matrix is one of the most common tasks while working with linear algebraic expressions. We can find the inverse of only those matrices which are square and whose determinant is non-zero.

In R, the inverse of a matrix can be calculated using the solve() function. The inverse of a matrix A is a matrix A^-1 such that A * A^-1 = I, where I is the identity matrix.

Here's an example of how to calculate the inverse of a matrix in R: 

# create a 2x2 matrix
A <- matrix(c(1, 2, 3, 4), nrow = 2)

# calculate the inverse of A
A_inv <- solve(A)

# print the inverse of A
A_inv

The solve() function takes the matrix as its argument and returns the inverse of the matrix. In this example, the matrix A is a 2x2 matrix with elements 1, 2, 3, and 4. The solve() function is used to calculate the inverse of A, which is then stored in the variable A_inv. The result is a 2x2 matrix with elements -2, 1.5, 1, and -0.5.

It's important to note that not all matrices have an inverse. A matrix is invertible only if its determinant is not zero. If the determinant of a matrix is zero, it's called a singular matrix and it doesn't have an inverse.