# NCERT Class 12-Mathematics: Exemplar Chapter –3 Matrices Part 12

Doorsteptutor material for CBSE/Class-12 Business-Studies is prepared by world's top subject experts: fully solved questions with step-by-step explanation- practice your way to success.

Download PDF of This Page (Size: 127K) ↧

**Question 31:**

Show that if A and B are square matrices such that , then

.

**Answer:**

By matrix multiplication we can write:

We know that matrix multiplication is not commutative but it is given that:

…proved

**Question 32:**

Let , and .

Show that:

(a)

(b)

(c)

(d)

(e)

(f)

(g)

(h)

(i)

**Answer:**

We have, , and

(i)

And

Hence proved.

(ii)

And

Also,

Hence Proved.

(iii)

Hence Proved.

(iv)

And

Also

Hence Proved.

(v)

Now,

A. Hence Proved.

(vi)

And

Hence proved.

(vii)

Now,

Hence Proved.

(viii)

Now,

And

[Using Eq. (ii) and (iii)]

[Using Eq. (i)] Hence proved

(ix)

Hence proved.