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Exercise - 4.2

Determinants

**Question-1 :-**
Using the property of determinants and without expanding, prove that:

**Question-2 :-**
Using the property of determinants and without expanding, prove that:

**Question-3 :-**
Using the property of determinants and without expanding, prove that:

**Question-4 :-**
Using the property of determinants and without expanding, prove that:

**Question-5 :-**
Using the property of determinants and without expanding, prove that:

**Question-6 :-**
Using the property of determinants and without expanding, prove that:

**Question-7 :-**
Using the property of determinants and without expanding, prove that:

**Question-8 :-**
Using the property of determinants, prove that:

(i)

(ii)

**Question-9 :-**
Using the property of determinants, prove that:

**Question-10 :-**
Using the property of determinants, prove that:

(i)

(ii)

**Question-11 :-**
Using the property of determinants, prove that:

(i)

(ii)

**Question-12 :-**
Using the property of determinants, prove that:

**Question-13 :-**
Using the property of determinants, prove that:

**Question-14 :-**
Using the property of determinants, prove that:

**Question-15 :-**
Let A be a square matrix of order 3 × 3, then |kA| is equal to

(A) k|A| (B) k²|A| (C) k^{3}|A| (D) 3k|A|

A is a square matrix of order 3 × 3. The correct answer is C.

**Question-16 :-**
Which of the following is correct

(A) Determinant is a square matrix.

(B) Determinant is a number associated to a matrix.

(C) Determinant is a number associated to a square matrix.

(D) None of these

We know that to every square matrix, A = [aij] of order n. We can associate a number called the determinant of square matrix A, where aij = (i, j)th element of A. Thus, the determinant is a number associated to a square matrix. The correct answer is C.

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