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Jun 14th, 2015

we use the notation A^{-1}
to denote the inverse of matrix A. Some important things to remember
about inverse matrices is they are not commutative, and a full
generalization is possible only if the matrices you are using a square.
(meaning they have the same number of rows and columns, an n x n matrix)

An n x n matrix (A) is said to be invertible if there is an n x n matrix (C) such that CA= I and AC= I where I is the n x n identity matrix. An identity matrix is a square matrix with ones on the diagonal and zeros elsewhere.

Basically A^{-1} A= I and A A^{-1} = I where A is an invertible matrix and A^{-1}
is the inverse of A. A matrix is said to be a singular matrix if it is
non-invertible. A matrix is a nonsingular matrix if it is an invertible
matrix.
A simple formula for finding the inverse of a 2 x 2 matrix is given by Theorem 4:
We call the quantity ad - bc the determinant of the matrix. (
det A = ad - bc ) A 2 x 2 matrix is invertible if and only if (iff) its
determinant does not equal 0.