List of top Mathematics Questions on Matrices and Determinants asked in CUET (UG)

If \( A=\begin{bmatrix}2 & 3 \\ 5 & -2\end{bmatrix} \), then:

A die is thrown again and again until three 5's are obtained. The probability of obtaining the third 5 in the seventh throw of the die is:

Let \(A\) and \(B\) be two \(3\times3\) matrices such that \[ A^2-4A+3I=O \] and \[ B=A^{-1}+2A. \] Find the determinant of \(B\) if \(\det(A)=3\).

Given a matrix \(A\) of order \(3\times3\). If \[ |A|=3 \] then the value of \[ |A(\operatorname{adj}A)| \] is:

Let $A$ be a $3 \times 3$ matrix such that $A^2 = I$. If $\det(A) = -1$ and the sum of eigenvalues is $1$, find the set of eigenvalues of $A$.

If \[ A = \begin{bmatrix}2 & 1 \\ 3 & 4\end{bmatrix} \] then find \( |A| \).

Match the following:

If \( A \) is a square matrix of order 3 such that its determinant value is \( |A| = -2 \), find the value of the scalar-scaled determinant \( |4A| \).

If \( A \) is a square matrix of order \( 3 \) such that \( |2(\text{adj}\,A)| = 288 \), then the possible value of the determinant \( |A| \) is:

Let \( A \) be a non-singular \( 3 \times 3 \) matrix satisfying the equation \( A^3 - 6A^2 + 11A - 6I = O \). If \( B = A^2 - 5A + 7I \) and \( \det(A) = 6 \), then the value of \( \det(B) \) is equal to:

The function \[ f:\mathbb R\to\mathbb R,\qquad f(x)=|x| \] (\(\mathbb R\) is the set of real numbers) is:

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:

Let \(A\) be a non-singular \(3\times3\) matrix satisfying \[ A^3-6A^2+11A-6I=O. \] If \[ B=A^2-5A+7I, \] then find \(\det(B)\) given that \(\det(A)=6\).

The value of \( \lambda \) for which the following system of equations has unique solution: \[ \lambda x+3y-z=1 \] \[ x+2y+z=2 \] \[ -\lambda x+y+2z=-1 \] are:

Let A = [aij]n x n be a matrix. Then Match List-I with List-II
List-I
(A) AT = A
(B) AT = -A
(C) |A| = 0
(D) |A| $\neq$ 0
List-II
(I) A is a singular matrix
(II) A is a non-singular matrix
(III) A is a skew symmetric matrix
(IV) A is a symmetric matrix
Choose the correct answer from the options given below:

If A = $\begin{bmatrix} 0 & -1 \\ 1 & 0 \end{bmatrix}$ and B = $\begin{bmatrix} 1 & 0 \\ 1 & 0 \end{bmatrix}$ then the matrix AB is equal to

If A = $\begin{bmatrix} 0 & 0 & \sqrt{3} \\ 0 & \sqrt{3} & 0 \\ \sqrt{3} & 0 & 0 \end{bmatrix}$, then |adj A| is equal to

If A is a square matrix and I is the identity matrix of same order such that A2 = I, then (A - I)3 + (A + I)3 - 3A is equal to

If P, Q and R are three singular matrices given by \(P = \begin{bmatrix} 2 & 3a \\ 4 & 3 \end{bmatrix}\), \(Q = \begin{bmatrix} b & 5 \\ 2a & 6 \end{bmatrix}\) and \(R = \begin{bmatrix} a^2 + b^2 - c & 1-c \\ c+1 & c \end{bmatrix}\), then the value of \((2a + 6b + 17c)\) is

Let A = [aij]2x3 and B = [bij]3x2, then |5AB| is equal to

If A and B are invertible matrices then which of the following statement is NOT correct?

Let AX = B be a system of three linear equations in three variables. Then the system has
(A) a unique solution if |A| = 0
(B) a unique solution if |A| $\neq$ 0
(C) no solutions if |A| = 0 and (adj A) B $\neq$ 0
(D) infinitely many solutions if |A| = 0 and (adj A)B = 0
Choose the correct answer from the options given below:

If A is a square matrix and I is the identity matrix of same order such that A2 = I, then (A - I)3 + (A + I)3 - 3A is equal to

If A and B are skew-symmetric matrices, then which one of the following is NOT true?

Let A be a non-singular matrix of order 3 and \(|A| = 15\), then \(|\text{adj } A|\) is equal to