# NCERT Class 12-Mathematics: Exemplar Chapter – 3 Matrices Part 12 (For CBSE, ICSE, IAS, NET, NRA 2022)

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**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.