The nxn matrix with 1’s on the diagonal and zeros elsewhere is the nxn ….

the identity matrix can be either a square matrix or not a square matrix

A(BC) = (AB)C

A(B+C) = AB + AC

A^3 = A.A.A

A^0 =

AX = I, so A is invertible

AX = I, so X is the inverse of A

AX = I, so A and X have the same size

if AX = I, then XA = I

AX = I, then A and X are squared matrices

in 2x2 matrix if ad-bc = 0 The matrix can has an inverse

to get the inverse of A 2x2 matrix we can use this formula: 1/ad-bc .B where B is the same as A with swapping diagonal elements and multiply non-diagonal elements by -1, and to make sure that ad-bc not equal to 0

If A is invertible, the reduced row-echelon form of A is I

if A is invertible AX = b has exactly one solution for every nx1 vector b

if A is invertible AX = 0 has exactly one solution (namely trivial solution x=0)

if A is invertible then AX = b has exactly one solution namely A^-1 .b

if A isn’t invertible, then AX = b has either infinite solutions or no solutions

(A^-1)^-1 =

(5A)^-1 = 1/5 A^-1

(AB)^-1 =