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

If $\begin{bmatrix} 2 & 3 \\ 5 & 7 \end{bmatrix} \begin{bmatrix} 1 & -3 \\ -2 & 4 \end{bmatrix} = \begin{bmatrix} -4 & 6 \\ -9 & x \end{bmatrix}$, then the value of $x$ is:

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

For a $3 \times 3$ matrix $A$, if $A(\operatorname{adj} A) = \begin{bmatrix} 99 & 0 & 0 \\0 & 99 & 0 \\0 & 0 & 99 \end{bmatrix}$, then $\det(A)$ is equal to:

If $A$ is a non-singular square matrix of order 3 and $|A^{-1}| = 24$, then the value of $|2A(\operatorname{adj}(3A))|$ is:

If $ A $ is a square matrix such that $ \text{adj}(\text{adj}(A)) = A $, then $ |A| $ is:

For a matrix $ A $ of order $ 3 \times 3 $, which of the following is true?

If $ A $ is a square matrix such that $ \text{adj}(\text{adj}(A)) = A $, then $ |A| $ is:

If $A$ is a square matrix of order 3 and $A \cdot (\operatorname{Adj}(A)) = 10I$, then the value of $\frac{1}{25} |\operatorname{adj}(A)|$ is:

For a matrix $ A $ of order $ 3 \times 3 $, which of the following is true?

If $A$ is a square matrix of order 3 such that $|A| = 2$, then $|\operatorname{adj}(\operatorname{adj}(A))|$ is:

The function $f(x) = \begin{vmatrix} x^{2} & x \\ 3 & 1 \end{vmatrix}, x \in \mathbb{R}$ has:

If $A, B$ are symmetric matrices of the same order, then $AB - BA$ is a:

If $ A = \begin{bmatrix} -k & 0 \\ 0 & -k \end{bmatrix}, \, k \neq 0 $, then the value of $ m $ in $ (A^T)^4 = mA $ is:

$\text{ If } \Delta = \begin{vmatrix} 1 & \cos x & 1 \\ -\cos x & 1 & \cos x \\ -1 & -\cos x & 1 \\ \end{vmatrix} , \text{ then:}$
$(A)\space \Delta = 2(1 - \cos^2 x)$
$(B)\space \Delta = 2(2 - \sin^2 x)$
(C) Minimum value of ∆ is 2
(D) Maximum value of $ \Delta $ is 4

For $ I = \begin{bmatrix} 1 & 0 \\ 0 & 1 \end{bmatrix} $, if $ A = \begin{bmatrix} a & b \\ c & -a \end{bmatrix} $ be such that $ A^2 = I $, then: