Say, You have two matrices P and Q. Matrix division is the process of multiplying matrix P with inverse of matrix Q.

Hearing matrix division, you may think of dividing corresponding elements of two matrices. But, that's not the case. There is no such thing as matrix division (by dividing corresponding elements) in linear algebra.

Instead, matrix division is referred to multiplication of the first matrix with inverse of second matrix. That is, P * Q^-1

For example, when we divide 12 ÷ 3. We are actually multiplying 12 with inverse of 3, which is 1/3. So, 12 ÷ 3 = 12 * 1/3 = 4

Same way, matrix division is the multiplication of first matrix with inverse of second matrix. That is, P * Q^-1

There is a rule for matrix division. Not so much rules, but a requirement.

Suppose you want to divide matrix K by matrix L. The requirement is that 1. matrix L should be a square matrix (to find the inverse of L).

2. L should be a non-singular matrix, meaning its determinant cannot be zero

3. Both these condition should hold true, only then division is possible. Otherwise, matrix division is not possible.

To divide two matrices. You need to multiply the first matrix with inverse of the second matrix

For example, two matrices J and K.

To divide J by K, you need to multiply J with inverse of K. That is J • K^-1

The formula for matrix division is

R = H/K = H * K^-1

Where R is the result of division of matrix H by matrix K

Matrix division with different dimensions is not possible. The dimensions of both matrices should be same to perform matrix division.

Its because the inverse of a matrix is only possible if the matrix is a square matrix. And, square matrix has same number of rows and columns.

So, to divide two matrices, the dimensions of both matrices should be same.