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Let $A = \begin{bmatrix} 1 & -3 \\ 1 & 2 \end{bmatrix}$, $B = \begin{bmatrix} 4 & 6 \\ -2 & 2 \end{bmatrix}$ and $C$ be a matrix such that $C = AB$. Then $|(BC)^{-1}|$ is equal to

If $A = \begin{bmatrix} 2 & 1 & -1 \\ 0 & 3 & -2 \\ k & 1 & 0 \end{bmatrix}$ is non-singular matrix, then the value(s) of $k$ belongs to:

[Where $R$ is the set of real numbers]

Let $A = \begin{bmatrix} 0 & 2y & z \\ x & y & -z \\ x & -y & z \end{bmatrix}$ and $I$ be an identity matrix of order 3. If $A^TA=I$, then $x^2+y^2+z^2$ is equal to:

Let $A=[a_{ij}]$ be a matrix of order $3 \times 4$ such that $a_{ij}=\begin{cases}2i-3j, & i \ge j \\ 3i+j, & i<j\end{cases}$ then the sum of all the elements of the first two rows of this matrix is:

If $A=\begin{bmatrix} x & p & x+p \\ y & q & y+q \\ z & r & z+r \end{bmatrix}$, then $|A|$ is

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

Let $A=\begin{bmatrix}1 & 0 \\ -1 & 7\end{bmatrix}$ and $B=\begin{bmatrix}0 & 4 \\ -1 & 7\end{bmatrix}$ then

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$\begin{vmatrix} a & b-c & c+b \\ a+c & b & c-a \\ a-b & a+b & c \end{vmatrix}$ is equal to:

Let $A=\begin{bmatrix}2 & 2 & 2 \\ 0 & 2 & 2 \\ 0 & 0 & 2\end{bmatrix}$, then $A^6$ is equal to:

Let $A=\begin{bmatrix}a & 0 \\ b & 0\end{bmatrix}$ and $A^2=\begin{bmatrix}4 & c \\ 2 & 0\end{bmatrix}$, $a,b,c \in \mathbb{Z}$. Then the minimum value of $a+b+c$ is:

If A is a non-singular matrix of order 3, then

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If $A=\begin{bmatrix}3 & -2 & 3 \\ 2 & 1 & -1 \\ 4 & -3 & 2\end{bmatrix}$ and $A(adjA)=xI$, where $I$ is an identify matrix of order 3, then $x$ is equal to

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If $A=\begin{bmatrix}2 & -1 & 3 \\ -3 & 4 & 5\end{bmatrix}$ and $B=\begin{bmatrix}2 & 1 \\ 3 & 5 \\ 2 & 3\end{bmatrix}$ and $BA=(b_{ij})$, then $b_{22}+b_{31}$ is :

Which of the following are correct?

(A) If $A=\begin{bmatrix}7 & 5 \\ 4 & 3\end{bmatrix}$, then $A^{-1}=\begin{bmatrix}3 & -5 \\ -4 & 7\end{bmatrix}$

(B) If $A=\begin{bmatrix}3 & 5 \\ 6 & 10\end{bmatrix}$, then $A$ is a non-singular matrix

(C) $A=\begin{bmatrix}0 & -5 \\ 5 & 3\end{bmatrix}$ is a symmetric matrix

(D) If $A=\begin{bmatrix}6 & x \\ y & 0\end{bmatrix}$ and $A=A^T$, then $x=y$

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The real value of $a$ for which the system of equations $x+ay=0, y+az=0, z+ax=0$ has infinitely many solutions, is :

If A and B are symmetric matrices of the same order then which of the following statements are correct?

A. AB is symmetric matrix

B. AB - BA is skew symmetric matrix

C. $B^TAB$ is symmetric matrix

D. $A - A^T$ is skew symmetric matrix

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If $A = \dfrac{1}{9}\begin{bmatrix} -8 & 1 & 4 \\ 4 & 4 & 7 \\ 1 & -8 & 4 \end{bmatrix}$, then

(Where $A^{-1}$ and $A^T$ represent inverse and transpose of matrix $A$ respectively)

If a matrix $A = \begin{bmatrix} x+3 & 3 \\ 2x+1 & 5 \end{bmatrix}$ is singular , then the value of $x$ will be

If $[2x \quad 4]\begin{bmatrix} x \\ -8 \end{bmatrix} = [0]$, then the value of $x$ is/are

A. $-4$

B. $4$

C. $16$

D. $-16$

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If A is a square matrix of order 4 and $|adj\,A| = 8$, then $|A| =$

Which of the following statements are correct ?

A. If the product of 2 non-zero square matrices is a zero matrix, then either A is singular or B is singular

B. If A is a non singular matrix , then $|A^{-1}| = \dfrac{1}{|A|}$

C. If A is an invertible square matrix then $adj\,A^T = \dfrac{1}{adj\,A}$

D. If A and B are invertible matrices then $(AB)^{-1} = B^{-1}A^{-1}$

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The value/s of '$\lambda$' for which the system of equations

$\lambda x + 3y - z = 1$

$x + 2y + z = 2$

$-\lambda x + y + 2z = -1$

has unique solution is/are:

(where $R$ is set of real numbers)

The matrix $\begin{bmatrix} 0 & 0 & 1 \\ 0 & 1 & 0 \\ 1 & 0 & 0 \end{bmatrix}$ is

If $\begin{vmatrix} 1 & x & x^2 \\ x^2 & 1 & x \\ x & x^2 & 1 \end{vmatrix} = (x^{\lambda}-1)^{\mu}$ then the value of $\lambda$ and $\mu$ are given by

If A is a square matrix of order 3 such that $|A| = 3$, then the value of $|adj\,A| + |adj\,(adj\,A)|$ is

If $A = \begin{bmatrix} 9 & 7 & 5 \\ 6 & 4 & 2 \\ 1 & 3 & 8 \end{bmatrix}$, then (cofactor of $a_{13}$ - cofactor of $a_{32}$ )will be equal to :

Match the LIST-I with LIST-II

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If $A = \begin{bmatrix} 1 & 0 \\ -1 & 7 \end{bmatrix}$ is a matrix such that $A^2 = 8A + KI$,where $I$ is an identity matrix of order 2 then value of $K$ is :

If A is a skew-symmetric matrix then, the matrix $B^TAB$ is:-