Introduction To Matrices - JEE Chapter Free MCQ Test with solutions

The number of elements for a matrix with the order m×n is equal to mn, where m is the number of rows and n is the number of columns in the matrix.

= x+10 = 3x+4
= x = 3

The number of possible entries of 2 × 2 matrix is 4 Every entry has two choice, 0 or 1.

Thus, the total no. of choices is,

2 × 2 × 2 × 2 = 2⁴

= 16

Given:

 A and B be two non zero square matrics

Calculations:

Matrix AB is defined means Columns is equal to the Rows of B 

and BA is defined means Columns of B is equal to the Rows of A

Hence, Both matrices (A) and (B) have same order is Correct.

A matrix having non-zero elements only in the diagonal running from the upper left to the lower right.

The given matrix is a diagonal matrix. 

Rows are represented by i
Columns are represented by j
^._.. a = (i+3)(j-1)
i = 2 , j = 1    (given)
a₂₁ = (2+3)(1-1) = 0
so, a₂₁ = 0

Calculation:

Given: A is a matrix of order 3 × 5 and B is a matrix of order 5 × 3

Number of rows in A = 3

Number of column in A = 5

Number of rows in B = 5

Number of column in B = 3

The order of AB = number of row is A × number of columns in B
= 3 × 3
And, 
The order of BA = number of row is B × number of columns in A
= 5 × 5
Hence, option (3) is correct.

The information is represented in the form of a 3 X 2 matrix as follows:

The entry in the third row and second column represents the number of women workers in factory III.

Let A and B be two matrices such that AB =A and BA=B Now, consider AB=A Take Transpose on both side (AB)^T=A^T
⇒A^T=B^T⋅A^T ...(1)
Now, BA=B
Take, Transpose on both side (BA)^T=B^T
⇒ B^T=A^T⋅B^T…(2)
Now, from equation (1) and (2). we have A^T=(A^T.B^T)A^T
A^T=A^T(B^TA^T)
=A^T(AB)^T(∵(AB)^T=B^T=B^TA^T)
=A^T⋅A^T
Thus, A^T=(A^T)²