Fsc Part 1 Mathematics (Complete Solution)

Q6
If A and B are square matrices of the same order , then explain why in general

(i) (A+B)2≠A2+2AB+B2

Solution:

L.H.S= (A+B)2

=(A+B)(A+B)

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

=A2+A.B+B.A+B2

As we know that matrix does not has commutative property therfore A.B≠B.A

Hence it is clear that (A+B)2≠A2+2AB+B2

(ii) (A-B)2≠A2-2AB+B2

Solution:

L.H.S= (A-B)2

=(A-B)(A-B)

=A(A-B)-B(A-B)

=A2-A.B-B.A+B2

As we know that matrix does not has commutative property therfore A.B≠B.A

Hence it is clear that (A+B)2≠A2+2AB+B2

 

(iii) (A+B)(A-B)≠A2-B2

Solution:

L.H.S=(A+B)(A-B)

      =A(A-B)+B(A-B)

     =A.A-A.B+B.A-B.B

          =A2-A.B+B.A-B2

As we know that matrix does not has commutative property therfore A.B≠B.A

Hence it is clear that (A+B)(A-B)≠A2-B2

 

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