Matrix Division: Technically, there is no such thing as matrix division. Dividing a matrix by another matrix is an undefined function. The closest equivalent is multiplying by the inverse of another matrix. In other words, while [A] ÷ [B] is undefined, you can solve the problem [A] * [B]-1. Since these two equations would be equivalent for scalar quantities, this “feels” like matrix division, but it’s important to use the correct terminology. It is important to note that [A] * [B]-1 and [B]-1 * [A] are not the same problem.
There are several constraint for a matrix to be invertible.
- Matrix has to be a square: To take the inverse of a matrix, it must be a square matrix, with the same number of rows and columns. If the matrix you’re planning to inverse is non-square, there is no unique solution to the problem
- A matrix that has an inverse is called “invertible” or “non-singular.” Matrices without an inverse are “singular
- Two matrices can be multiplied together: To multiply two matrices together, the number of columns in the first matrix must equal the number of rows in the second matrix.If this does not work in either arrangement ([A] * [B]-1 or [B]-1 * [A]), there is no solution to the problem.
- Matrix must have a non-zero determinant
So, the direct division of two matrices might not be available but we can get a solution depending upon the certain conditions are met.