(ii) Since, the order of the matrix is 3 × 4, so there are 3 × 4 = 12 elements in it.
1 × 24, 2 × 12, 3 × 8, 4 × 6, 6 × 4, 8 × 3, 12 × 2 or 24 × 1.
Similarly, a matrix containing 13 elements can have order 1 × 13 or 13 × 1.
1 × 18, 18 × 1, 2 × 9, 9 × 2, 3 × 6, 6 × 3
Similarly, a matrix containing 5 elements can have order 1 × 5 or 5 × 1

as the given matrices are equal, their corresponding elements are equal. Comparing the corresponding elements, we get
x+ y = 6 ……(i)
5 + z = 5 ……(ii)
And xy = 8 …..(iii)
From eq. (ii), we get z = 0
From eq. (i), y = 6-x …..(iv)
Substituting the value of y in eq. (iii), we obtain
x(6-x) = 8 → x2 -6x+8 = 0
→ (x-2)(x-4) = 0 → x=2 or x=4
When x=2, then from eq. (iv), y = 6-2 = 4 and
When x=4, then from eq. (iv), y = 6-4 = 2
So, either x=2, y=4 and z=0
Or x=4, y=2 and z=0
as the given matrices are equal, their corresponding elements are equal. Comparing the corresponding elements, we get
x+y+z = 9 …..(i)
x+z = 5 ……..(ii)
y+z = 7 ……….(iii)
Subtracting eq. (ii) from eq. (i), we get y=4
Subtracting eq. (iii) from eq. (i), we get x=2
Substituting y=4 in eq. (iii), we get
4+z = 7 → z = 7-4 = 3
Hence, x = 2, y = 4, z = 3

By definition of equality of matrix as the given matrices are equal, their corresponding elements are equal. Comparing the corresponding elements, we get
a-b = -1 …….(i)
2a-b = 0 …….(ii)
2a+c = 5 …….(iii)
and 3c+d = 13 …….(iv)
Subtracting eq. (i) from eq. (ii), we get a = 1
Putting a = 1 in eq. (i) and eq. (iii), we get
1-b = -1 and 2+c = 5
→ b = 2 and c = 3
Substituting c = 3 in eq. (iv), we obtain
33+d = 13 → d = 13-9 = 4
Hence, a=1, b=2, c=3 and d=4
Therefore, A=
So, correct option is (c)

Since, x can have only one value at a time. Hence, it is not possible to find the values of x and y for which the given matrices are equal.
So, correct option is (b).
Note: Sometimes on solving an equation, we get more than one values of the variables. This means that such a matrix does not exist.
- 27 (b) 18 (c) 81 (d) 512
Hence, all the nine entries can be chosen in 29 = 512 ways.
(By the multiplication principle)
Required number of the matrices in 512. So, the correct option is (d).