top of page # Suppose a vector V is transformed by matrix M1  to generate vector VT. # ​Further VT is transformed by M2to generate vector VTT. # ​If V is transformed by Mto generate vector VTT directly. # Here transformation M is same as combined effect of transformation M2  performed after transformation M1. M is referred as multiplication of matrices M1  and M2 . # Suppose matrix M1  and M2  are:  # First and second column of matrix M1 represents transformation of unit vector i and j respectively. Further when transformation M2 is performed, overall effect of the two will change the unit vectors to  # iT and jT represent first and second column respectively of overall transformation matrix i.e. product matrix of M1 and M2. # This way, direction of transformation remain same but magnitude gets multiplied by k times. • # Multiplication of matrix is not commutative, since applying transformation M1 after M2 is not same as applying transformation M2 after M1. • # Matrix multiplication is associative. • # Transpose of product shows following relation: bottom of page