List of top Mathematics Questions on Matrices asked in CBSE CLASS XII

Let \[ A = \begin{pmatrix} 1 & 4 \\ -2 & 1 \end{pmatrix} \quad \text{and} \quad C = \begin{pmatrix} 3 & 4 & 2 \\ 12 & 16 & 8 \\ -6 & -8 & -4 \end{pmatrix}. \] Then, find the matrix $B$ if $AB = C$.

If $A$ and $B$ are two square matrices each of order 3 with $|A| = 3$ and $|B| = 5$, then $|2AB|$ is:

Let $ A = \begin{bmatrix} 1 & -2 & -1 \\ 0 & 4 & -1 \\ -3 & 2 & 1 \end{bmatrix}, B = \begin{bmatrix} -5 \\ -2 \end{bmatrix}, C = [9 \ \ 7], $ which of the following is defined?

If $ A $ is a square matrix of order 2 such that $ \text{det} = 4 $, then $ \text{det}(4 \, \text{adj} \, A) $ is equal to:

If \[ A = \begin{bmatrix} 1 & 2 & 0 \\ -2 & -1 & -2 \\ 0 & -1 & 1 \end{bmatrix} \] then find $ A^{-1} $. Hence, solve the system of linear equations: \[ x - 2y = 10, \] \[ 2x - y - z = 8, \] \[ -2y + z = 7. \]

If A and B are square matrices of same order such that AB = BA, then $A^2 + B^2$ is equal to :

Let $ A $ be a matrix of order $ m \times n $ and $ B $ be a matrix such that $ A^T B $ and $ B A^T $ are defined. Then, the order of $ B $ is:

If $M$ and $N$ are square matrices of order 3 such that $\det(M) = m$ and $MN = mI$, then $\det(N)$ is equal to :

If $\begin{bmatrix} 2x-1 & 3x \\ 0 & y^2 - 1 \end{bmatrix}$ is a matrix, then the value of $(x - y)$ is:

If A and B are invertible matrices of order $3 \times 3$ such that $\text{det} = 4$ and $\text{det}([AB]^{-1}) = \frac{1}{20}$, then $\text{det}$ is equal to:

A school wants to allocate students into three clubs: Sports, Music, and Drama, under the following conditions:
- The number of students in the Sports club should be equal to the sum of the number of students in the Music and Drama clubs.
- The number of students in the Music club should be 20 more than half the number of students in the Sports club.
- The total number of students to be allocated in all three clubs is 10.
Find the number of students allocated to different clubs, using the matrix method.}

If \[ A = \begin{pmatrix} -1 & 0 & 0 \\ 0 & 3 & 0 \\ 0 & 0 & 5 \end{pmatrix} \] then $A$ is a/an:

A furniture workshop produces three types of furniture: chairs, tables, and beds each day. On a particular day, the total number of furniture pieces produced is 45. It was also found that the production of beds exceeds that of chairs by 8, while the total production of beds and chairs together is twice the production of tables. Determine the units produced of each type of furniture, using the matrix method.

Let both $AB'$ and $B'A$ be defined for matrices $A$ and $B$. If the order of $A$ is $n \times m$, then the order of $B$ is:

If $ \begin{bmatrix} 7 & 0 \\ 0 & 7 \end{bmatrix} $ is a scalar matrix, then $ x^y $ is equal to:

If $ A $ and $ B $ are square matrices of order $ m $ such that $ A^2 - B^2 = (A - B)(A + B) $, then which of the following is always correct?

If $ A $ and $ B $ are square matrices of the same order, then $ (A B^T - B A^T) $ is a:

Four friends Abhay, Bina, Chhaya, and Devesh were asked to simplify $ 4 AB + 3(AB + BA) - 4 BA $, where $ A $ and $ B $ are both matrices of order $ 2 \times 2 $. It is known that $ A \neq B $ and $ A^{-1} \neq B $. Their answers are given as:

Which of the following can be both a symmetric and skew-symmetric matrix?

If \[ A = \begin{bmatrix} -1 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & 1 \end{bmatrix}, \text{ then } A^{-1} \text{ is:} \]

The matrix \[ \begin{pmatrix} 0 & 1 & -2 \\ -1 & 0 & -7 \\ 2 & 7 & 0 \end{pmatrix} \] is a :

Assertion (A): $ A = \text{diag} [3, 5, 2] $ is a scalar matrix of order $ 3 \times 3 $.
Reason (R): If a diagonal matrix has all non-zero elements equal, it is known as a scalar matrix.

If $ A $ and $ B $ are invertible matrices, then which of the following is not correct?

If $ A = \left[ \begin{array}{ccc} 5 & 0 & 0 \\ 3 & 0 & 5 \\ 0 & 0 & 5 \end{array} \right] $, then $ A^3 $ is:

If \[ A = \begin{bmatrix} 1 & 0 & 0 \\ 0 & 5 & 0 \\ 0 & 0 & -2 \end{bmatrix}, \] then $ |A| $ is: