English
Hindi
Bengali
Tamil

Question

Download Solution PDF

Let A be a non-singular matrix of the order 2 × 2 then |A-1| =

  1. |A|
  3. 0
  4. None of these

Answer (Detailed Solution Below)

Option 2 :
Free Tests
View all Free tests >
Free
CRPF Head Constable & ASI Steno (Final Revision): Mini Mock Test
40 Qs. 40 Marks 45 Mins
Start Now

Detailed Solution

Download Solution PDF

Concept:

The determinant of the inverse of an invertible matrix is the inverse of the determinant: 

Explanation:

Let A is the second-order matrix,

As we know, AA-1 = I

Taking determinants both sides, we get

⇒ det (AA-1) = det I

⇒ det(A-1) × det (A) = 1              [∵ det (AB) = det A × det B]

∴ det(A-1) =  

Download Solution PDF
Latest Indian Coast Guard Navik GD Updates

Last updated on Jun 11, 2025

-> The Indian Coast Guard Navik GD is a prestigious exam for those who want to serve the country in Defence Services.

-> A total of 260 vacancies have been released through the Coast Guard Enrolled Personnel Test (CGEPT) for the 01/2026 and 02/2026 batch.

-> Candidates can apply online from 11th to 25th June 2025.

-> Candidates who have completed their 10+2 with Maths and Physics are eligible for this post. 

-> Candidates must go through the Indian Coast Guard Navik GD previous year papers.

Exams Tests Super Practice

More Determinants Questions

Q1.If the system of linear equations 2x + 2ay + az = 0 2x + 3by + bz = 0 2x + 4cy + cz = 0, where a, b, c ∈ R are non-zero and distinct; has non-zero solution, then
Q2.Let A and B be two square matrices of order 3 such that |A| = 3 and |B| = 2. Then |AT A(adj(2A))–1 (adj(4B))(adj(AB))–1AAT | is equal to : 
Q3.If the system of equations  11x + y + λz = –5 2x + 3y + 5z = 3 8x – 19y – 39z = µ has infinitely many solutions, then λ4 – µ is equal to :
Q4.Let A be the square matrix of order 3, then |kA|, where k is a scalar, is equal to: 
Q5.Which one of the following options is incorrect?  For a square matrix A in the matrix equation AX = B. 
Q6.The area of the triangle (in unit2) whose vertices are A(4, 8),B(-6, 2) and C(5, 4) is: 
Q7.If \(\rm A=\begin{bmatrix}1&2&3\\\ 3&4&5\\\ 5&6&7\end{bmatrix}\) and \(\rm B=\begin{bmatrix}1&1&1\\\ 2&2&2\\\ 3&3&3\end{bmatrix}\), then det(A + B) = ?
Q8.The product of the cofactors of 3 and -2 in the matrix \(\begin{bmatrix}1&0&-2\\\ 3&-1&2\\\ 4&5&6\end{bmatrix}\) is:
Q9.The value of the determinant \(\left|\begin{array}{lll}b^2-a b & b-c & b c-a c \\ a b-a^2 & a-b & b^2-a b \\ b c-a c & c-a & a b-a^2\end{array}\right|\) = ?
Suggested Test Series
View All >
Coast Guard Navik GD (General Duty) 02/2025 Mock Test Series
384 Total Tests with 3 Free Tests
Start Free Test
ICG Navik GD (01/2026 - 02/2026) Mock Test Series
252 Total Tests with   2 Free Tests
Start Free Test

Indian Coast Guard Navik GD Important Links

Admit CardEligibility CriteriaSalary & Job ProfileSyllabus and Exam PatternCut OffExam Analysis

More Mathematics Questions

Q1.log10 10000 = _______?
Q2.Consider a system equation \(2x+y-z=0\), \(4x - py + 4z = 4\) and \(x-y+z=q\) where \(p, q \in I\) and \(p, q \in [1, 10]\), then identify the correct statement(s).   List-I List-II (I) Number of ordered pairs \((p, q)\) for which system of equation has unique solution is (P) 1 (II) Number of ordered pairs \((p, q)\) for which system of equation has no solution is (Q) 9 (III) Number of ordered pairs \((p, q)\) for which system of equation has infinite solution is (R) 91 (IV) Number of ordered pairs \((p, q)\) for which system of equation has atleast one solution is (S) 90
Q3.Match List I with List II:   List - I List - II (I) The number of solutions of the equation\((1 - \cos 2x)(\cos 2x + \cot^2 x) = 0\) where \(0 \le x \le 2\pi\) is (P) 4 (II) \(\tan 81^\circ - \tan 63^\circ - \tan 27^\circ + \tan 9^\circ\) equals (Q) 3 (III) The number of solutions of (x, y), which satisfy |y| = sin x and y = cos-1(cos x), where -2π ≤ x ≤ 2π is (R) 2 (IV) For the equation \(\cos^{-1}x + \cos^{-1}2x + \pi = 0\), the number of real solutions is (S) 1     (T) 0  
Q4.If Σn = 36, find n
Q5.If log 2 = 0.2614, log 3 = 0.3521, log 6 = ?
Q6.The growth model for a population is Nt = N0ert where Nt is the population at time t, N0 is the initial population and r is the per capita growth rate. How long does it take for the population numbers to double?
Q7.Suppose that the growth rate of the number of individuals (N) in a population in an environment with a carrying capacity K is modelled as \(\frac{d N}{d t}=r N \frac{K-N}{K}\) where r is the per capita growth rate and t is time; r and K are positive constants. At which of the following values of N will the population growth rate be the maximum?
Q8.The shadow of a vertical pole, formed due to a nearby lamp which is at a height of 12 m, measures 4 m. If the lamp is moved horizontally 2 m further away from the pole, the length of the shadow measures 8 m. What is the height (in m) of the pole?
Q9.A pack of cards contains 4 aces, 4 kings, 4 queens and 4 jacks. Out of these 16 number of cards, two cards are drawn at random. Find the probability that at least one of them is an ace :
Q10.If the equations 2x2 + kx - 5 = 0 and x2 - 3x - 4 = 0 have one root common, then find the value of k.
Testbook Edu Solutions Pvt. Ltd.
1st & 2nd Floor, Zion Building,
Plot No. 273, Sector 10, Kharghar,
Navi Mumbai - 410210
support@testbook.com
Toll Free:1800 833 0800
Office Hours: 10 AM to 7 PM (all 7 days)
Company
About usCareers We are hiringTeach Online on TestbookPartnersMediaSitemap
Products
Test SeriesTestbook PassOnline CoursesOnline VideosPracticeBlogRefer & EarnBooks
Copyright © 2014-2022 Testbook Edu Solutions Pvt. Ltd.: All rights reserved
User PolicyTermsPrivacy
Hot Links： teen patti gold download apk teen patti master online teen patti yas