A is correct: (AB)−1=B−1A−1 is a standard property. B is incorrect: (A+B)−1=B−1+A−1 in general. C is correct: adj(A)=∣A∣⋅A−1 follows from A⋅adj(A)=∣A∣I. D is correct: det(A−1)=1/det(A)=(detA)−1. So A, C and D only are correct.
CUET UG 2022 — Mathematics Algebra
Let A and B be two non-singular, square matrices of same order, and
A. (AB)−1=B−1⋅A−1
B. (A+B)−1=B−1+A−1
C. adj.A=∣A∣⋅A−1
D. det(A−1)=[detA]−1
Choose the correct answer from the options given below
Held on 10 Aug 2022 · Verified 13 Jul 2026.
A and B only
B and C only
B and D only
A, C and D only
Sign in to track your attempts and accuracy.
Sign in to keep a private note on this question. Nothing you write is ever public.
If f(x) = 2x + 3, then f⁻¹(x) is:
A relation R in the set A = {1, 2,3, 4} is given by R = {(1,1), (2,2), (1,2), (2,3), (3,4), (4,4), (1,3), (2,4), (1,4)} is
If $P(A) = \frac{3}{5}$, $P(B) = \frac{1}{2}$ and $P(A \cap B) = \frac{1}{4}$, then $P(\overline{A} | \overline{B})$ is
If corner points of the bounded feasible region are (0, 0), (3, 0) and (0, 3) and objective function is $z = 4x + 7y$, then the maximum value of $z$ is
The maximum value of a LPP $z = 3x + 4y$ subject to the constraints: $x + y \leq 6$, $x \geq 0$, $y \geq 0$ is:
Work through every CUET UG Algebra PYQ, year by year.