Algebra

Matrices & Determinants

Medium

applied

If the matrix $\begin{bmatrix} z & x-y+2 & x+4y-3 \\ x+y & 0 & a-3 \\ 2x-y+3 & a-1 & 0 \end{bmatrix}$ is skew-symmetric, then the value of $(a+x+y+z)$ is:

✅ Correct Option: 3

Skew-symmetry forces zero diagonal, so $z=0$ . Comparing $a_{12}=-a_{21}$ gives $x-y+2=-(x+y)$ , so $x=-1$ . Comparing $a_{13}=-a_{31}$ gives $3x+3y=0$ , so $y=1$ . Comparing $a_{23}=-a_{32}$ gives $a-3=-(a-1)$ , so $a=2$ . Hence $a+x+y+z=2$ .

2025: 14 May Shift 2

If the matrix $\begin{bmatrix} 0 & 1 & 4x\ \\ -1 & 0 & -5 \\ 2 & 5 & y \end{bmatrix}$ is skew-symmetric, then

2025: 27 May Shift 1

If A is a square matrix such that $A^2 = A$ and I is the identity matrix of the same order as A, then $(I+A)^2-3A$ is equal to

2025: 19 May Shift 1

Which of the following statements are correct?

(A) If A is a square matrix, then $|A^2| = |A|^2$ .

(B) If A and B are square matrices of the same order, then det (AB) = det (A) + det (B).

(D) If the matrix $\begin{bmatrix} 5 -x & x -1 \\ 3 &5 \end{bmatrix}$ is singular, then the value of x is 7/2.

Choose the correct answer from the options given below:

2025: 30 May Shift 2

If $\begin{bmatrix}2x+1 & 5x \\ 0 & y^2+1\end{bmatrix} = \begin{bmatrix}x+3 & 10 \\ 0 & 26\end{bmatrix}$ then the possible values of x + y are:

2022: 16 July Shift 2

The number of all possible matrices of order 3 x 3 with each entry belonging to the set {0, 1} is:

2026: 29 May Shift 2

Given that $[a_{ij}]$ is a square matrix of order n.

Match the LIST-I with LIST-II

LIST-I		LIST-II
A.	$A=[a_{ij}]; a_{ij}=\begin{cases}1, & \forall i=j\\0, & \forall i\neq j\end{cases}$	I. Identity Matrix
B.	$B=[a_{ij}]; a_{ij}=\begin{cases}2i-3j, & \forall i=j\\0, & \forall i\neq j\end{cases}$	II. Diagonal Matrix
C.	$C=[a_{ij}]; a_{ij}=\begin{cases}k, & \forall i=j\\0, & \forall i\neq j\end{cases}$	III. Scalar Matrix
D.	$D=[a_{ij}]; a_{ij}=\begin{cases}2i-3j, & \forall i\leq j\\0, & \forall i>j\end{cases}$	IV. Upper Triangular Matrix

Choose the correct answer from the options given below:

If the matrix [zx−y+2x+4y−3x+y0a−32x−y+3a−10]\begin{bmatrix} z & x-y+2 & x+4y-3 \\ x+y & 0 & a-3 \\ 2x-y+3 & a-1 & 0 \end{bmatrix}​zx+y2x−y+3​x−y+20a−1​x+4y−3a−30​​ is skew-symmetric, then the value of (a+x+y+z)(a+x+y+z)(a+x+y+z) is:

Solution

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CUET Mathematics Past Year Questions (Topic-Wise)

If the matrix $\begin{bmatrix} z & x-y+2 & x+4y-3 \\ x+y & 0 & a-3 \\ 2x-y+3 & a-1 & 0 \end{bmatrix}$ is skew-symmetric, then the value of $(a+x+y+z)$ is: