# NCERT Class 12-Mathematics: Exemplar Chapter – 3 Matrices Part 9 (For CBSE, ICSE, IAS, NET, NRA 2022)

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**Question 20**:

If , then find a non-zero matrix C such that .

**Answer**:

We have,

Let is a non-zero matrix of order .

And

For

On using equality of matrix, we get

We see that on taking C of order We get

In general,

Where, is any real number.

**Question 21**:

Give an example of matrices A, B and C such that , where A is nonzero matrix, but .

**Answer**:

Thus, we see that [using Eq. (i) and (ii) ]

Where, A is non-zero matrix but .

**Question 22**:

If

(i)

(ii) .

**Answer**:

We have,

(i)

And

Again,

[using Eq. (i) and (ii) ]

(ii)

And

Also

And

From Eq. (iii) and (iv) ,

**Question 23**:

If prove that

**Answer**:

And

Thus, we see that, [using Eq. (i) and (ii) ]

Hence Proved.