Q. 83.6( 7 Votes )

If and verify that A(B – C) = (AB – AC).

Answer :


Given : and


Matrix A is of order 3 3; matrix B is of order 3 3 and matrix C is of order 3 3


To verify : A(B – C) = (AB – AC).


The formula used : 3x3-matrix-formula.png


If A is a matrix of order a b and B is a matrix of order c d ,then matrix AB exists and is of order a d ,if and only if b = c


If A is a matrix of order a b and B is a matrix of order c d ,then matrix BA exists and is of order c b ,if and only if d = a


B - C = =


B - C =


For Matrix A(B - C), a = 3,b = c = d = 3,thus matrix A(B + C) is of order 3 x 3


A(B - C) =


A(B - C) =


A(B - C) = =


A(B - C) =


For matrix AB, a = 3, b = c = d = 3 ,matrix AB is of order 3 x 3


Matrix AB =


Matrix AB =


Matrix AB = =


Matrix AB =


For matrix AC, a = 3, b = c = d = 3 ,matrix AC is of order 3 x 3


Matrix AC =


Matrix AC =


Matrix AC = =


Matrix AC =


Matrix AB - AC = =


Matrix AB - AC =


A(B – C) = (AB – AC) =


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