in multiplying row vector by a column vector, they must have the same number of entries

A mxr . B rxn =

Cij =

to multiply two matrices A and B, (A.B) the number of columns of .. must be the equal the number of rows of …

Resulting matrix of multiplying A and B (A.B) has the same number of rows as .. and the same number of columns as ..

A.0 =

A.I =

I.A =

I^2 =

In general A.B = B.A

In matrices Multiplication is commutative

A.I = I.A = A

I is called

In general, just because AX = BX, we cannot conclude that A = B

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