# NCERT Class 12-Mathematics: Exemplar Chapter –4 Determinants Part 14

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**Question 46:**

____________.

**Answer:**

**Question 47:**

If ________.

**Answer:**

Zero

## State True or False for the Statements of the Following Exercises

**Question 48:**

, where A is a square matrix and .

**Answer: True**

**Question 49:**

where is any real number and A is a square matrix.

**Answer: False**

**Question 50:**

, where A is non-singular matrix.

**Answer: False**

**Question 51:**

If A and B are matrices of order 3 and , then .

**Answer: True**

**Question 52:**

If the value of a third order determinant is, then the value of the determinant formed by replacing each element by its co-factor will be .

**Answer: True**

**Question 53:**

, where *a*, *b*, *c* are in A.P.

**Answer: True**

**Question 54:**

, where A is a square matrix of order two.

**Answer False**

**Question 55:**

The determinant is equal to zero.

**Answer: True**

**Question 56:**

If the determinant splits into exactly K determinants of order 3, each element of which contains only one term, then the value of K is 8.

**Answer: True**

**Question 57:**

Let

**Answer: True**

**Question 58:**

The maximum value of is .

**Answer: True**