CUET Mathematics: AlgebraMatrices & Determinants. Free, no login required.

If A and B are invertible matrices of the same order, then,

Match List-I with List-II

Choose the correct answer from the options given below:

If A is a square matrix such that $A^2 = I$, then $(A+I)^3 + (A-I)^3 - 7A$ is equal to

Which of the following are true about the properties of transpose of appropriate matrices?

A. $(A+B)^T = A^T + B^T$

B. $(A-B)^T = A^T - B^T$

C. $(AB)^T = A^TB^T$

D. $(kA)^T = k(A^T)$, where k is a scalar

Choose the correct answer from the options given below:

Given that $Y_{3\times k}$, $W_{n\times 3}$ and $P_{p\times k}$ are matrices of specified order, then the condition for n, p, k so that $3PY + 2WY$ is well defined, is:

If $A = \begin{bmatrix} 1 & 0 \\ -1 & 7 \end{bmatrix}$, $I = \begin{bmatrix} 1 & 0 \\ 0 & 1 \end{bmatrix}$, then the value of k so that $A^2 = 8A + kI$ is

If $A = \begin{bmatrix} a & b \\ c & \frac{1+bc}{a} \end{bmatrix}$, then $aA^{-1}$ is equal to which of the following? [I is the identity matrix of order 2]

If $A = \begin{bmatrix} 2 & -3 & 5 \\ 6 & 0 & 4 \\ 1 & 5 & -7 \end{bmatrix}$, then which of the following statements are TRUE?

[where $A_{ij}$ is the cofactor of the (i, j)th element, $a_{ij}$ of matrix A, $1 \gt i, j \le 3$.]

(A) $a_{11}A_{31} = -24$

(B) $a_{12}A_{32} = -66$

(C) $a_{13}A_{33} = -90$

(D) $a_{21}A_{21} = -24$

Choose the correct answer from the options given below:

If $A = \begin{bmatrix} 1 & -3 \\ 2 & 0 \end{bmatrix}$, then which of the following statement(s) is/are TRUE?

(A) Matrix A is non-singular

(B) $|3A| = 54$

(C) $|adjA| = 36$

(D) $A^2 = \begin{bmatrix} -5 & -3 \\ 2 & -6 \end{bmatrix}$

Choose the correct answer from the options given below:

Let A (1, 3), B (0, 0) and C (k, 0) be three points such that area of $\Delta(ABC) = 3$ sq. units, then the value of k is:

If A is a 3-rowed square matrix and $|A| = 5$, then $|adjA|$ is equal to

The matrix X such that it satisfies the equation: $X\begin{bmatrix} 3 & 2 \\ 1 & -1 \end{bmatrix} = \begin{bmatrix} 4 & 1 \\ 2 & 3 \end{bmatrix}$ is

If $P = \begin{bmatrix} 1 & 2 \\ -1 & 3 \end{bmatrix}$, $Q = \begin{bmatrix} 4 & 0 \\ 1 & 5 \end{bmatrix}$ and $R = \begin{bmatrix} 2 & 0 \\ 1 & -2 \end{bmatrix}$, then which of the following are TRUE?

(A) $(P^T)^T = P^T$

(B) $(P-Q)R = PR - QR$

(C) $(P-Q)^T = Q^T - P^T$

(D) $(PQ)^T = Q^TP^T$

Choose the correct answer from the options given below:

Let A be the matrix $\begin{bmatrix} 3 & -4 \\ 1 & -1 \end{bmatrix}$. If A is expressed as the sum of P and Q, where P is a symmetric and Q is a skew symmetric matrix, then which of the following options define P and Q correctly?

Which of the following are TRUE?

(A) The inverse of $\begin{bmatrix} 3 & -3 \\ 2 & 7 \end{bmatrix}$ is $\frac{1}{27}\begin{bmatrix} 7 & 3 \\ -2 & 3 \end{bmatrix}$.

(B) The determinant of $\begin{bmatrix} 3 & -3 \\ 2 & 7 \end{bmatrix}$ is 29.

(C) The inverse of $\begin{bmatrix} 3 & -3 \\ 2 & 7 \end{bmatrix}$ is $\frac{1}{29}\begin{bmatrix} 7 & 3 \\ -2 & 3 \end{bmatrix}$.

(D) The adjoint of $\begin{bmatrix} 3 & -3 \\ 2 & 7 \end{bmatrix}$ is $\begin{bmatrix} 7 & 3 \\ -2 & 3 \end{bmatrix}$.

Choose the correct answer from the options given below:

If $A = \begin{bmatrix} 1 & 2 & -3 \end{bmatrix}$ and $B = \begin{bmatrix} 1 & 3 \\ 7 & -8 \\ 1 & 2 \end{bmatrix}$, then which of the following are true?

(A) AB is a $2 \times 3$ matrix

(B) $B^2$ is a $3 \times 3$ matrix

(C) BA is not possible

(D) $A^3$ is not possible

Choose the correct answer from the options given below:

Given a matrix $A = \begin{bmatrix} 0 & 3 & -8 \\ -3 & 0 & 13 \\ 8 & -13 & 0 \end{bmatrix}$. Which of the following statements is/are TRUE?

(A) The matrix A is a skew-symmetric matrix.

(B) The matrix A is a symmetric matrix.

(C) The matrix A is a singular matrix.

(D) The matrix A is a non-singular matrix.

Choose the correct answer from the options given below:

If $A^T = \begin{bmatrix} a & b \\ c & d \end{bmatrix}$ and $A^{-1} = \begin{bmatrix} p & q \\ r & s \end{bmatrix}$, then

Match List-I with List-II

Choose the correct answer from the options given below:

If $A = \begin{bmatrix} 3 & 0 & -1 \\ 2 & 3 & 0 \\ 0 & 4 & 1 \end{bmatrix}$, then which of the following is/are correct ?

A. $|A| = 1$

B. $A$ is singular matrix.

C. $|adj A| = 1$

D. $|adj.(adj A)| = 1$

Choose the correct answer from the options given below:

If $\begin{vmatrix} x & 3 & x \\ x^2 & x & 7 \\ x & x & 7 \end{vmatrix} = ax^4+bx^3+cx^2+dx+e$, then the value of $6a+5b+4c+3d+2e$ is

If $A=\begin{bmatrix} 1 & 0 \\ -1 & 5 \end{bmatrix}$ and I is indentity matrix of order 2, then which of following statements are TRUE?

A. $A^2-6A-mI=0$ if $m=-5$.

B. $A^2-6A+mI=0$ if $m=-5$.

C. $A$ is a non-singular matrix.

D. $A^2=A$

Choose the correct answer from the options given below:

If a matrix $A=\begin{bmatrix} 3 & -5 & 7 \\ 5 & 2 & 4 \\ -7 & -4 & 9 \end{bmatrix}$ is expressed as the sum of a symmetric matrix P and a skew symmetric matrix Q, then symmetric matrix P will be

If $A=\begin{bmatrix} 0 & -\tan\alpha/2 \\ \tan\alpha/2 & 0 \end{bmatrix}$, then the value of $\begin{bmatrix} \cos\alpha & -\sin\alpha \\ \sin\alpha & \cos\alpha \end{bmatrix}$ for all $\alpha \in \mathbb{R}$(set of real numbers), is

(I is identity matrix of order 2)

$A=\begin{bmatrix} 0 & 1 & 3 \\ 1 & 2 & x \\ 2 & 3 & 1 \end{bmatrix}$ and $2B=\begin{bmatrix} 1 & -8 & 5 \\ -1 & 6 & -3 \\ 1 & 2y & 1 \end{bmatrix}$. If $A=B^{-1}$ then $x+y$ is equal to

If $\begin{vmatrix} m! & (m+1)! & (m+2)! \\ (m+1)! & (m+2)! & (m+3)! \\ (m+2)! & (m+3)! & (m+4)! \end{vmatrix} = 2k$, where $m$ is a positive integer then which of the following are factors of $k$?

A. $m!$

B. $(m+1)!$

C. $(m+2)!$

D. $(m+3)!$

Choose the correct answer from the options given below:

If $\Delta$ represents the value of the determinant $\begin{vmatrix} 1 & \sin k\theta & 1 \\ -\sin k\theta & 1 & \sin k\theta \\ -1 & -\sin k\theta & 1 \end{vmatrix}$, where $k$ is any real number then the value of $\Delta$ belongs to

If $x,y,z$ are non-zero real numbers such that $\begin{vmatrix} 10+x & 10 & 10 \\ 10 & 10+y & 10 \\ 10 & 10 & 10+z \end{vmatrix}=0$, then the value of $x^{-1}+y^{-1}+z^{-1}$ is

For the matrix $A=\begin{bmatrix} 0 & 0 & 5 \\ 0 & 6 & 0 \\ 7 & 0 & 0 \end{bmatrix}$, which of the following statement(s) is/are TRUE ?

A. $A$ is a scalar matrix.

B. $A$ is a diagonal matrix.

C. $A$ is a square matrix.

D. $A$ is a skew symmetric matrix.

Choose the correct answer from the options given below:

If $\begin{bmatrix} x-2y & z \\ 3x+y & w \end{bmatrix}=\begin{bmatrix} 1 & 2 \\ -11 & 1 \end{bmatrix}$; then the value of $y-x$ is:-

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