Algebra

Matrices & Determinants

Easy

core

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

5/2

$2\sqrt{2}$

✅ Correct Option: 3

For a square matrix of order $n$ , $|adj\,A| = |A|^{n-1}$ .

With $n=4$ this gives $|A|^3 = 8$ .

Hence $|A| = 2$ .

2022: 25 May Shift 1

Which of the following statements is NOT CORRECT.

2026: 29 May Shift 1

Match List-I with List-II

List-I (Singular matrix)	List-II (A value of $x$ )
(A) $A=\begin{bmatrix}x & 4 \\ 2 & 2x\end{bmatrix}$	(I) 3
(B) $A=\begin{bmatrix}3 & x \\ 3x & 9\end{bmatrix}$	(II) 4
(C) $A=\begin{bmatrix}x & 1 \\ 1 & x\end{bmatrix}$	(III) 2
(D) $A=\begin{bmatrix}x & 1 \\ 16 & x\end{bmatrix}$	(IV) 1

Choose the correct answer from the options given below:

2025: 30 May Shift 2

The diagonal elements of a skew symmetric matrix are all

2022: 10 Aug Shift 1

The length ( $x$ ) and breadth ( $y$ ) of plot satisfy equations:

2025: 27 May Shift 1

If $\begin{vmatrix} p-a & 0 & c-r \\ 0 & q-b & c-r \\ a & b & r \end{vmatrix} = 0$ , then the value of $\dfrac{p}{p-a} + \dfrac{q}{q-b} + \dfrac{r}{r-c}$ is

2026: 25 May Shift 1

Which of the following statements are TRUE?

A. If the product of two matrices is a zero matrix, it is not necessary that one of the matrix is a zero matrix.

B. For any three matrices A, B and C, $(AB)C = A(CB)$ .

C. Diagonal elements of a skew symmetric matrix can be non-zero.

D. Multiplication of diagonal matrices of same order is always commutative.

Choose the correct answer from the options given below:

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

Solution

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CUET Mathematics Past Year Questions (Topic-Wise)

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