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 2 proportional rows or 2 proportional columns then det(A) = …

det(kA) =

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

det(A.B) = det(A). det(B) [Same Size]

A invertible then det(A)^-1 = 1/det(A)

The transpose of the cofactors matrix is named

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

in Cramer’s law x1 = det(A)/det(A1)

A is nxn matrix then Ax = 0 has only the trivial solution

A is nxn matrix then the reduced row-echelon form of A is I

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