We know from yesterday that, to prove that a matrix is an inverse, the matrix and it's inverse must be multiplied together, and the answer must be an identity matrix (1's on the main diagonal, 0's everywhere else).
Today, we calculated the inverse of a given matrix. As we know, the word "inverse" in math means the opposite, so the answer that we calculate will be a matrix that is, mathematically, opposite from the one that we started with.
To do this, we
1. find the determinant of the matrix (remember, the matrix must be a perfect square!)
2. multiply every element in the matrix by (1/determinant). This means that, in many cases, the inverse matrix will contain fractions/decimals in it.
The answer is your inverse matrix!
The only time that this DOESN'T work is when your determinant is zero, because (1/0) is undefined.
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