**NCERT Exemplar Problems Class 12 Mathematics Chapter 3 Matrices**

**Short Answer Type Questions**

**Long Answer Type Questions**

**Objective Type Questions**

**Fill In the Blanks Type Questions**

**True/False Type Questions**

**82. A matrix denotes a number.**

** Sol.** False

A matrix is an ordered rectangular array of numbers of functions.

**83. Matrices of any order can be added.**

** Sol.** False

Two matrices are added, if they are of the same order.

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

** Sol.** False

If two matrices have same number of rows and same number of columns, we cannot say two matrices are equal as their corresponding elements may be different.

**85. Matrices of different order cannot be subtracted.**

** Sol.** True

Two matrices of same order can be subtracted

**86. Matrix addition is associative as well as commutative.**

** Sol.** True

Matrix addition is associative as well as commutative i.e.,

(A + B) + C = A + (B + C) and A + B = B + A, where A, B and C are matrices of same order.

**87. Matrix multiplication is commutative.**

** Sol.** False

If AB is defined, it is not necessary that BA is defined.

Also if AB and BA are defined, it not”necessary that they have same order. Further if AB and BA are defined and have same order, it is not necessary their corresponding elements are equal.

So, in general AB^BA

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

** Sol.** False

Since, in an identity matrix, the diagonal elements are one and rest are all zero.

**89. If A and B are two square matrices of the same order, then A + B = B + A.**

** Sol.** True

Since, matrix addition is commutative i.e., A + B = B +A, where A and B are two square matrices.

**90. If A and B are two matrices of the same order, then A-B = B-A.**

** Sol.** False

A-B = -(B-A)

Thus A-Bâ‰ B-A

However when A – B = B – A

A-B = 0 or A =B

**92. Transpose of a column matrix is a column matrix. False**

** Sol**.Transpose of a column matrix is a row matrix.

**93. If A and B are two square matrices of the same order, then AB = BA. False**

** Sol.**For two square matrices of same order it is not always true that AB = BA.

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