If A is not invertible, then AX = b has no solution

If A is n x n invertible matrix, then KA is invertible for any nonzero scalar n; (KA)^-1 = (1/k)A^-1

if a product AB is not invertible, then A or B is not invertible.

if A or B are invertible, then AB can be invertible in one case

det(A) = …. A is a 2x2 matrix

A^-1 = 1/det(A) [d -b -c a]

det(A) =

det(A), A is a

if A is a square matrix, then the minor of entry aij is denoted by Mij and is defined to be determinant of the submatrix that remains after the ith row, and the jth column are deleted from A

The number (-1)^i+j Mij is denoted by Cij and is called the cofactor of entry aij

if A is an n x n matrix, then the number obtained by multiplying the entries in any row or column of A by corresponding cofactors and adding the resulting products is called the determinant of A, the sums themselves are called cofactor expansions of A

the best strategy for cofactor expansion is to expand along a row or a column with the most zeros

if A is an nxn triangular matrix (upper triangle matrix, lower triangle matrix, diagonal) then det(A) is the product of the entries on the main diagonal of the matrix

the arrow technique can work with 4x4 or higher matrices in finding the determinant

if A has a row of zeros or a column of zeros then the det(A) = 0

if A is a square matrix then det(A) .. det(A)T

In matrix B the first row of A was multiplied by k then

In the matrix B the first and second rows of A were interchanged

in the matrix B a multiple of the second row of A was added to the first row