# NCERT Class 12-Mathematics: Exemplar Chapter – 3 Matrices Part 7 (For CBSE, ICSE, IAS, NET, NRA 2023)

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**Question 12**:

Find the matrix A satisfying the matrix equation:

**Answer**:

We have,

On adding Eqs. (i) and (iv) , we get

On adding Eqs. (ii) and (iii) , we get

On adding Eqs. (vi) and (iv) , we get

From eqs. (v) and (vii)

Now, using the values of a and d in Eq. (iii) , we get

Now, using the values of a and d in Eq. (ii) , we get

On multiplying Eq. (ix) by 5 and Eq. (x) by 13, then adding, we get

**Question 13**:

Find A, if

**Answer**:

Let

**Question 14**:

If , then verify

**Answer**:

We have,

And

Also,

So is not possible, since the B is not a square matrix.

Hence,