# NCERT Class 12-Mathematics: Exemplar Chapter – 3 Matrices Part 23 (For CBSE, ICSE, IAS, NET, NRA 2022)

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**Question 81**:

In applying one or more row operations while finding by elementary row operations, we obtain all zeros in one or more, then ________.

**Answer**:

Does not exist

## State Exercises 82 to 101 Which of the Following Statements Are True or False

**Question 82**:

A matrix denotes a number.

**Answer: False**

**Question 83**:

Matrices of any order can be added.

**Answer: False**

**Question 84**:

Two matrices are equal if they have same number of rows and same number of columns.

**Answer: False**

**Question 85**:

Matrices of different order can-not be subtracted.

**Answer: True**

**Question 86**:

Matrix addition is associative as well as commutative.

**Answer: True**

**Question 87**:

Matrix multiplication is commutative.

**Answer: False**

**Question 88**:

A square matrix where every element is unity is called an identity matrix.

**Answer: False**

**Question 89**:

If A and B are two square matrices of the same order, then .

**Answer: True**

**Question 90**:

If A and B are two matrices of the same order, then .

**Answer: False**

**Question 91**:

If matrix , then or or both A and B are null matrices.

**Answer: False**

**Question 92**:

Transpose of a column matrix is a column matrix.

**Answer: False**

**Question 93**:

If A and B are two square matrices of the same order, then .

**Answer: False**

**Question 94**:

If each of the three matrices of the same order are symmetric, then their sum is a symmetric matrix.

**Answer: True**

**Question 95**:

If A and B are any two matrices of the same order, then .

**Answer: False**

**Question 96**:

If , where A and B are not square matrices, then number of rows in A is equal to number of columns in B and number of columns in A is equal to number of rows in B.

**Answer: Ture**

**Question 97**:

If A, B and C are square matrices of same order, then always implies that .

**Answer: False**

**Question 98**:

is always a symmetric matrix for any matrix A.

**Answer: True**

**Question 99**:

If , then AB and BA are defined and equal.

**Answer: False**

**Question 100**:

If A is skew symmetric matrix, then is a symmetric matrix.

**Answer: True**

**Question 101**:

, where A and B are invertible matrices satisfying commutative property with respect to multiplication.

**Answer: True**