det(A) =

det(A), A is a

if A has a row of zeros or a column of zeros then the det(A) = 1

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

If A is a square matrix with two proportional rows or two proportional columns, then det (A) = 1

det(kA) =

det(A+B) != det(A) + det(B)

If A and B are square matrices of the different size, then det (A.B)= det (A) . det (B)

If A is invertible, then det(A)^-1 = 1/det(A)

in Cramer’s law x1 = det(A)/det(A1)

if A is a squared matrix then Ax = b is consistent for every nx1 matrix b

if A is a squared matrix then Ax = b has only one solution for every nx1 matrix b

A is nxn matrix then Ax = 1 has only the trivial solution