Q:

# What is a method for dividing matrices?

A:

A matrix is an arrangement of values that can be added, subtracted or multiplied by similar or corresponding matrices. Unfortunately, you cannot directly divide one matrix by another, but you can multiply a matrix by the inverse of another matrix in place of division.

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1. ### Make sure the inverse can be taken and multiplied

In order to be multiplied, the number of columns of the first matrix must be the same as the number of rows in the second matrix. The inverse of a matrix can only be taken when the matrix is a square. The inverse of a matrix has the same dimensions. The divided matrix must have a number of rows equal to the first matrix's columns.

2. ### Take the inverse of the second matrix

The inverse of a matrix is the matrix that would create the identity matrix if multiplied. The identity matrix is a square array that has values of 1 along the diagonal starting from the upper left, and values of 0 everywhere else. One trick for taking the inverse of a 2 x 2 matrix is to multiply one over the determinant of that matrix by the adjugate. The determinant of a 2 x 2 matrix with respective values a, b, c and d is (ad-bc). The inverse of that coefficient is multiplied to and distributed throughout the adjugate, which lists d, (-b), (-c) and a.

3. ### Multiply the first matrix by the inverse you found

To multiply matrices, add the products of the corresponding values of the rows in the first matrix and the rows in the second matrix. In matrix division, the second matrix used is the inverse that was calculated.

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