CUET Mathematics 2026 31st May Shift 2 PYQs

For every square matrix $A$ of order $n\times n$, which of the following statements are correct ?

(A) $(adjA)A = A(adjA) = |A|I$, where $I$ is identity matrix of order n.

(B) $|kA|=k^n|A|$, k is any scalar.

(C) $|adjA|=|A|^n$

(D) $A^2=A$

Choose the correct answer from the options given below:

A is a square matrix of order 3 x 3, then

Match List-I with List-II

List-I	List-II
(A) $\left\vert \text{adj}A \right\vert$	(I) $\dfrac{1}{\left\vert A \right\vert}$
(B) $\left\vert A^{-1} \right\vert$	(II) $\left\vert A \right\vert^{4}$
(C) $\left\vert A.\text{adj}A \right\vert$	(III) $\left\vert A \right\vert^{3}$
(D) $\left\vert \text{adj}(\text{adj}A) \right\vert$	(IV) $\left\vert A \right\vert^{2}$

Choose the correct answer from the options given below:

If the system of linear equations

$x + 2y - 3z = 1$

$(2p+1)y + z = 2$

$3x + 3z = 5$

has a unique solution, then p can not be equal to