Multiple choice (Matrix)

Choose and write the correct option in the following question:(Class 12 matrix multiple choice question)

1.) If $A = \begin{bmatrix} 0 & 1 \\ 1 & 0 \end{bmatrix},$ Then $A^2$ is equal to

(a) $\begin{bmatrix} 0 & 1 \\ 1 & 0 \end{bmatrix}$

(b) $\begin{bmatrix} 1 & 0 \\ 1 & 0\end{bmatrix}$

(d) $\begin{bmatrix} 1 & 0 \\ 0 & 1\end{bmatrix}$

Answer (d)

2.) If $\begin{bmatrix} \cos\alpha & -\sin\alpha \\ \sin\alpha & \cos\alpha \end{bmatrix}$ , then $A + A' = I$ if the value of α is

(a) π/6 (b) π/3

Answer (b)

3.)If A and B are square matrices of the same order , then (A + B)(A – B) is equal to

(a) $A^2-B^2$ (b) $A^2 - BA - AB - B^2$

Answer (c)

4.) Total number of possible matrices of order 3×3 with each entry 2 or 0 is

(a) 9 (b) 27

Answer (d)

5.) The matrix $\begin{bmatrix} 0 & -5 & 8 \\ 5 & 0 & 12 \\ -8 & -12 & 0\end{bmatrix}$ is a

(a) Diagonal matrix (b) Symmetric matrix

Answer (c)

Assume X, Y, Z, W and P are matrices of order 2×n,3×k, 2×p, n×3 and p×k respectively. Choose the correct option in (6) and (7)

6.) The restriction on n, k and p so that PY + WY willbe defined are

(a) k = 3, p = n (b) k is arbitrary, p = 2

Answer (a)

7.) If n = p then the order of the matrix 7X – 5Z is

(a) p×2 (b) 2×n

Answer (b)

8.) If $\begin{bmatrix} 2x + y & 4x \\5x - 7 & 4x \end{bmatrix} = \begin{bmatrix} 7 & 7y - 13 \\ y & x+6\end{bmatrix}$ , Then the value of x and y is

(a) x = 3, y = 1 (b) x = 2, y = 3

Answer (b)

9.) If A is matrix of order m×n and B is a matrix such that AB’ and B’A are both defined, the order of matrix B is

(a) m×m (b) n×n

Answer (d)

10.) If A and B are matrices of same order , then (AB’ – BA’) is a

(a) Skew symmetric matrix (b) Null matrix

Answer (a)

11.) If $A = \begin{bmatrix} \alpha & \beta \\ \gamma & -\alpha \end{bmatrix}$ is such that $A^2 = I$ , then

(a) I + α² + βγ = 0 (b) I – α² + βγ = 0

Answer (c)

12.) A matrix $A = [a_{ij}]_{3\times 3}$ is defined by

$a_{ij}=\left\{\begin{array}{l} 2i +3j, \text { if } i<j \\ 5, \text { if }i =j \\ 3i-2j, \text { if } i>j \end{array}\right\}$

The number of elements in A which are more than 5 is

(a) 3 (b) 4

Answer (b)

13.) If $A = \begin{bmatrix} 1 & a \\ 0 & 1 \end{bmatrix}$ , then $A^n$ (wher a∈ N) equals

(a) $\begin{bmatrix} 1 & na \\ 0 & 1 \end{bmatrix}$

(b) $\begin{bmatrix} 1 & n^2a \\ 0 & 1 \end{bmatrix}$

(d) $\begin{bmatrix} n & na \\ 0 & n \end{bmatrix}$

Answer (a)

14.) If A is a square matrix such that A² = I, then $(A-I)^3+(A+I)^3-7A$ is equal to

(a) A (b) I – A

Answer (a)

15.) If the matrix AB is zero, then

(a) It is not necessary that either A = O or B = O

(b) A = O or B = O

(d) All the statement are wrong

Answer (a)

16.) If $A = \begin{bmatrix} 2 & -1 & 3 \\ -4 & 5 & 1 \end{bmatrix}$ and $B = \begin{bmatrix} 2 & 3 \\ 4 & -2\\ 1 & 5\end{bmatrix}$ , then

(a) Only AB is defined (b) Only BA is defined

Answer (c)

17.) If A and B are symmetric matrices of the same order, then (AB’- BA’) is a

(a) Skew symmetric matrix (b) Null matrix

Answer (a)

18.) The matrix $\begin{bmatrix} 0 & 5 & -7 \\-5 & 0 & 11\\ 7 & -11 & 0 \end{bmatrix}$ is

(a) A Skew symmetric matrix (b) Null matrix

Answer (a)

19.) If A and B are two matrices of the order 3×m and 3×n respectively and m = n, then the order of matrix (5A – 2B) is

(a) m×3 (b) 3×3

Answer (d)

20.) If $A = \begin{bmatrix} 5 & x \\ y & 0\end{bmatrix}$ and A = A’, then

(a) x = 0, y = 5 (b) x + y = 5

Answer (c)

Multiple choice (Matrix)

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