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Multiplying by the inverse of a matrix is the closest thing we have to matrix division. Like multiplying a regular number by its reciprocal to get 1, multiplying a matrix by its inverse gives us the identity matrix (1 could be thought of as the "identity scalar").
This tutorial will walk you through this sometimes involved process which will become bizarrely fun once you get the hang of it.
Hint for finding the determinant of a 2x2 matrix
Find the determinant of a 2x2 matrix
Example of calculating the inverse of a 2x2 matrix
What the inverse of a matrix is. Examples of inverting a 2x2 matrix.
Find the inverse of a 2x2 matrix
Using the inverse of a matrix to solve a system of equations.
Using matrices to figure out if some combination of 2 vectors can create a 3rd vector
Find the determinant of a 3x3 matrix
Beginning our quest to invert a 3x3 matrix. We calculate the matrix of minors and the cofactor matrix.
Finishing up our 3x3 matrix inversion
Inverting a 3x3 matrix
Using Gauss-Jordan elimination to invert a 3x3 matrix.
When and why you can't invert a matrix.
Find the inverse of a 3x3 matrix