# Fill in the blank

(i) (AB)’ = ________.

(AB)’ = B’A’

Let A be matrix of order m× n and B be of n× p.

A is of order n× m and B is of order p× n.

Hence B A is of order p× m.

So, AB is of order m× p.

And (AB) is of order p× m.

We can see (AB) and B A are of same order p× m.

Hence (AB) = B A

Hence proved.

(ii) (kA)’ = ________. (k is any scalar)

If a scalar “k” is multiplied to any matrix the new matrix becomes

K times of the old matrix.

Eg: A =

2A =

=

(2A) =

A =

Now 2A =

=

Hence (2A) =2A

Hence (kA)’ = k(A)’

(iii) [k (A – B)]’ = ________.

A =

A =

2A = 2

=

B=

B =

2B =

=

A-B =

Now Let k =2

2(A-B) =

=

[2(A-B)] =

2A – 2B =

=

A – B =

=

2(A – B) = 2

=

Hence we can see [k (A – B)]’= k(A)’- k(B)’= k(A’-B’)

Rate this question :

How useful is this solution?
We strive to provide quality solutions. Please rate us to serve you better.
Try our Mini CourseMaster Important Topics in 7 DaysLearn from IITians, NITians, Doctors & Academic Experts
Dedicated counsellor for each student
24X7 Doubt Resolution
Daily Report Card
Detailed Performance Evaluation
view all courses
RELATED QUESTIONS :

<span lang="EN-USMathematics - Exemplar

<span lang="EN-USMathematics - Exemplar

Fill in the blankMathematics - Exemplar

Fill in the blankMathematics - Exemplar

Fill in the blankMathematics - Exemplar

If A, B are squarMathematics - Exemplar

Fill in the blankMathematics - Exemplar

Fill in the blankMathematics - Exemplar

Express the folloMathematics - Board Papers

Fill in the blankMathematics - Exemplar