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