If A is a square matrix of order 3 and |A| = 6, then the value of |adj A| is :
(a) 6
(b) 36
(c) 27
(d) 216
CBSE CLASS 12 • MATHEMATICS • CHAPTER 04
Determinants
17 distinct questions across 18 board paper set appearances (2022–2026).
If $A$ is a non-singular matrix, then which of the following is not true ?
(A) $\text{adj } A$ is singular
(B) $(\text{adj } A)^{-1} = (\text{adj } A^{-1})$
(C) $|A| \neq 0$
(D) $A^{-1}$ exists
If A is a non-singular matrix, then which of the following is not true ?
(A) adj A is singular
(B) (adj A)$^{-1} = (adj A^{-1})$
(C) $|A| \neq 0$
(D) A$^{-1}$ exists
If A is a non-singular matrix, then which of the following is not true ? (A) adj A is singular (B) $(\text{adj A})^{-1} = (\text{adj A}^{-1})$ (C) $|A| \neq 0$ (D) $A^{-1}$ exists
For a non-singular matrix X, if $X^2 = I$, then $X^{-1}$ is equal to :
(A) $X$
(B) $X^2$
(C) $I$
(D) $0$
For a non-singular matrix $\text{X}$, if $\text{X}^2 = \text{I}$, then $\text{X}^{-1}$ is equal to :
(A) $\text{X}$
(B) $\text{X}^2$
(C) $\text{I}$
(D) $0$
If $A$ is a square matrix of order $3$ such that $\det(A) = 9$, then $\det(9 A^{-1})$ is equal to
(A) $9$
(B) $9^{2}$
(C) $9^{3}$
(D) $9^{4}$
A system of linear equations is represented as $AX = B$, where $A$ is coefficient matrix, $X$ is variable matrix and $B$ is the constant matrix. Then the system of equations is
(A) Consistent, if $|A| \neq 0$, solution is given by $X = BA^{-1}$.
(B) Inconsistent if $|A| = 0$ and $(\text{adj } A) B =...
If A and B are invertible matrices, then which of the following is not correct?
(A) $(A + B)^{-1} = B^{-1} + A^{-1}$
(B) $(AB)^{-1} = B^{-1}A^{-1}$
(C) $\text{adj} (A) = |A| A^{-1}$
(D) $|A|^{-1} = |A^{-1}|$
If $A$ and $B$ are invertible matrices of order $3 \times 3$ such that $\det (A) = 4$ and $\det [(AB)^{-1}] = \frac{1}{20}$, then $\det (B)$ is equal to :
(A) $\frac{1}{20}$
(B) $\frac{1}{5}$
(C) 20
(D) 5
Let A be a square matrix of order 3. If $|A| = 5$, then $|\text{adj A}|$ is :
(A) 5
(B) 125
(C) 25
(D) -5
If $A$ and $B$ are non-singular matrices of same order with $\det(A) = 5$, then $\det(B^{-1}AB)^2$ is equal to (A) $5$ (B) $5^2$ (C) $5^4$ (D) $5^5$
Using determinants, find the area of $\Delta PQR$ with vertices $P(3, 1)$, $Q(9, 3)$ and $R(5, 7)$. Also, find the equation of line $PQ$ using determinants.
Assertion (A) : If $A$ is a square matrix of order $3$ such that $|adj A| = 144$, then the value of $|A|$ is $\pm 12$.
Reason (R) : If $A$ is an invertible matrix of order $n$, then $|adj A| = |A|^{n-1}$.
If A is a square matrix of order 3 and $|A| = 6$, then the value of $|\text{adj A}|$ is :
(a) $6$
(b) $36$
(c) $27$
(d) $216$
A professional typist having his shop in a busy market charges ₹ 200 for typing 8 English and 4 Hindi pages, while he charges ₹ 275 for typing 5 English and 10 Hindi pages. Based on the above information, answer the following questions : (i) If he charges ₹ x for one page of English and ₹ y for one ...
If A is a square matrix of order 3 and $|A| = 5$, then $|adjA| =$
(a) $5$ (b) $25$ (c) $125$ (d) $\frac{1}{5}$