# NCERT Class 12-Mathematics: Exemplar Chapter – 3 Matrices Part 8 (For CBSE, ICSE, IAS, NET, NRA 2023)

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**Question 15**:

If possible, find and , where

**Answer**:

We have,

So, AB and BA both are possible

[Since, in both A. B and B. A, the number of columns of first is equal to the number of rows of second.]

And

**Question 16**:

Show by an example that for .

**Answer**:

Let

Hence proved.

**Question 17**:

Given

**Answer**:

We have,

And

Also,

Thus, we see that,

**Question 18**:

Solve for *x* and *y*:

**Answer**:

We have,

And

On subtracting Eq. (i) and from (ii) , we get

**Question 19**:

If X and Y are matrices, then solve the following matrix equations for X and Y

**Answer**:

We have,

And

On subtracting Eq. (i) from Eq. (ii) , we get

On adding Eq. (i) and (ii) , we get

From Eq. (iv) ,