The number of all possible non-singular matrices of order 2 x 2 with each entry 0 or 1 is : Option 1: 4 Option 2: 7 Option 3: 6 Option 4: 5

Answer: 6. Solution: Total 2 x 2 matrices with entries 0 or 1: 2^4 = 16. For non-singular, = ad - bc ≠ 0. Case = 1: ad = 1, bc = 0 a=d=1 and (b,c) \(0,0),(0,1),(1,0)\: 3 matrices. Case = -1: ad = 0, bc = 1 b=c=1 and (a,d) \(0,0),(0,1),(1,0)\: 3 matrices. Total = 6.

Algebra

Matrices & Determinants

Medium

The number of all possible non-singular matrices of order $2 \times 2$ with each entry 0 or 1 is :

✅ Correct Option: 3

Total $2 \times 2$ matrices with entries 0 or 1: $2^4 = 16$ .

For non-singular, $\det = ad - bc \neq 0$ .

Case $\det = 1$ : $ad = 1, bc = 0 \Rightarrow a=d=1$ and $(b,c) \in \{(0,0),(0,1),(1,0)\}$ : 3 matrices.

Case $\det = -1$ : $ad = 0, bc = 1 \Rightarrow b=c=1$ and $(a,d) \in \{(0,0),(0,1),(1,0)\}$ : 3 matrices.

Total = 6.

2026: 29 May Shift 2

If $A=\begin{bmatrix}1&1&1\\1&0&2\\3&1&1\end{bmatrix}$ and $B=\begin{bmatrix}-2&0&2\\5&-2&-1\\1&2&-1\end{bmatrix}$ such that AB=4I (where I is identity matrix) then solution of system of equations $x+y+z=6, x+2z=7, 3x+y+z=12$ is

2022: 16 July Shift 2

If P and Q are symmetric matrices of same order, then $(PQ - QP)$ is

2026: 18 May Shift 2

If $A=\begin{bmatrix} 2 & 1 \\ 7 & 5 \end{bmatrix}$ , then the value of $|A(adj A)|$ is

2026: 22 May Shift 2

Match List-I with List-II

List-I	List-II
(A) If $A = [a_{ij}]_{n \times n}$ , where $a_{ij} = \begin{cases}0, & i \ne j \\ k, & i=j, k\ne 0\end{cases}$ then A is ___	(I) Symmetric matrix
(B) If $A = [a_{ij}]_{2\times 2}$ , where $a_{ij} = \begin{cases}1, & i \ne j \\ 0, & i=j\end{cases}$ , then $A^2$ is ___	(II) Skew-Symmetric matrix
(C) If A and B are matrices of the same order, then $(AB^T - BA^T)$ is ___	(III) Identity matrix
(D) If A and B are symmetric matrices of the same order, then $(AB+BA)$ is ___	(IV) Scalar matrix

Choose the correct answer from the options given below:

2026: 25 May Shift 1

Which of the following statements are TRUE?

A. If the product of two matrices is a zero matrix, it is not necessary that one of the matrix is a zero matrix.

B. For any three matrices A, B and C, $(AB)C = A(CB)$ .

C. Diagonal elements of a skew symmetric matrix can be non-zero.

D. Multiplication of diagonal matrices of same order is always commutative.

Choose the correct answer from the options given below:

2026: 14 May Shift 2

Consider the system of equations $x+y+z=2, 2x+3y+2z=5, x+2y+\lambda z=\mu$ then which of the following statements are TRUE?

A. The system of equations has unique solution if $\lambda=2$ and $\mu\in\mathbb R$ (set of real number)

B. The system of equations is inconsistent if $\lambda=1$ and $\mu=1$

C. The system of equations is consistent if $\lambda=1$ and $\mu=1$

D. The system of equations is consistent if $\lambda=1$ and $\mu=3$

Choose the correct answer from the options given below:

The number of all possible non-singular matrices of order 2×22 \times 22×2 with each entry 0 or 1 is :

Solution

Related questions:

Keyboard Shortcuts

CUET Mathematics Past Year Questions (Topic-Wise)

The number of all possible non-singular matrices of order $2 \times 2$ with each entry 0 or 1 is :