If A=bmatrix4 & 1\\2 & 3bmatrix and B=bmatrix-2 & 3\\1 & 2bmatrix such that 2B-3A+X=0 then X is Option 1: bmatrix-16 & 3\\-4 & -5bmatrix Option 2: bmatrix16 & -3\\4 & 5bmatrix Option 3: bmatrix16 & 4\\-3 & 5bmatrix Option 4: bmatrix-16 & -4\\3 & -5bmatrix

Answer: bmatrix16 & -3\\4 & 5bmatrix. Solution: From 2B-3A+X=O we get X=3A-2B. Here 3A=bmatrix12&3\\6&9bmatrix and 2B=bmatrix-4&6\\2&4bmatrix, so X=bmatrix16&-3\\4&5bmatrix.

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If $A=\begin{bmatrix}4 & 1\\2 & 3\end{bmatrix}$ and $B=\begin{bmatrix}-2 & 3\\1 & 2\end{bmatrix}$ such that $2B-3A+X=0$ then $X$ is

$\begin{bmatrix}-16 & 3\\-4 & -5\end{bmatrix}$

$\begin{bmatrix}16 & -3\\4 & 5\end{bmatrix}$

$\begin{bmatrix}16 & 4\\-3 & 5\end{bmatrix}$

$\begin{bmatrix}-16 & -4\\3 & -5\end{bmatrix}$

✅ Correct Option: 2

From $2B-3A+X=O$ we get $X=3A-2B$ .

Here $3A=\begin{bmatrix}12&3\\6&9\end{bmatrix}$ and $2B=\begin{bmatrix}-4&6\\2&4\end{bmatrix}$ , so $X=\begin{bmatrix}16&-3\\4&5\end{bmatrix}$ .

2025: 19 May Shift 1

If A and B are square matrices of the same order 3, such that det (A) = 3 and AB = 3I, where I is an identity matrix of order 3. Then the value of det (B) is:

2026: 29 May Shift 1

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

2022: 17 Aug Shift 2

Match List - I with List - II.

List - I	List - II
(A) $A$ is a square matrix of order $3$ and $\lvert 2A \rvert = k\lvert A \rvert$ , then $k$ is	(I) $0$
(B) Value of $\begin{vmatrix}1 & a & b+c \\ 1 & b & c+a \\ 1 & c & a+b\end{vmatrix}$ is	(II) $3$
(C) Matrix $\begin{bmatrix}5-x & x+1 \\ 2 & 4\end{bmatrix}$ is singular, then $x =$	(III) $8$
(D) If $A = (a_{ij}) = \begin{bmatrix}5 & 3 & 8 \\ 2 & 0 & 1 \\ 1 & 2 & 3\end{bmatrix}$ , then the minor of the element $a_{23}$ is	(IV) $7$

Choose the correct answer from the options given below :

2023: 15 June Shift 2

Let $A = [a_{ij}]$ be a $2 \times 2$ matrix such that $a_{ij} = \frac{|-3i+j|}{2}$ then $a_{21}$ is :

2026: 29 May Shift 2

If A and B are square matrices of order 3×3 such that |A|=7 and |B|=6, then |B adj A| =

2025: 22 May Shift 1

The value(s) of $K$ , for which the system of linear equations $2x + y + z = 1, x + Ky - z = \frac{3}{2}$ and $3y - 5z = 9$ does not possess a unique solution is

If A=[4123]A=\begin{bmatrix}4 & 1\\2 & 3\end{bmatrix}A=[42​13​] and B=[−2312]B=\begin{bmatrix}-2 & 3\\1 & 2\end{bmatrix}B=[−21​32​] such that 2B−3A+X=02B-3A+X=02B−3A+X=0 then XXX is

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If $A=\begin{bmatrix}4 & 1\\2 & 3\end{bmatrix}$ and $B=\begin{bmatrix}-2 & 3\\1 & 2\end{bmatrix}$ such that $2B-3A+X=0$ then $X$ is