1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
Fiesta28 [93]
3 years ago
9

Show that if A is​ invertible, then det Upper A Superscript negative 1det A−1equals=StartFraction 1 Over det Upper A EndFraction

1 det A. What​ theorem(s) should be used to examine the quantity det Upper A Superscript negative 1det A−1​? Select all that apply. A. If A and B are ntimes×n ​matrices, then det ABequals=(det Upper A )(det A)(det Upper B )(det B). Your answer is correct.B. If one row of a square matrix A is multiplied by k to produce​ B, then det Upper Bdet Bequals=ktimes•(det Upper A )(det A). C. A square matrix A is invertible if and only if det Upper Adet Anot equals≠0. Your answer is correct.D. If A is an ntimes×n ​matrix, then det Upper A Superscript Upper Tdet ATequals=det Upper Adet A. Consider the quantity (det Upper A )(det Upper A Superscript negative 1 Baseline )(det A)det A−1. To what must this be​ equal? A. det Upper I
Mathematics
1 answer:
netineya [11]3 years ago
7 0

Answer:

Therefore  

 det(A)*det(A^{-1}) = 1      and         det(A^{-1}) = 1/det(A)

Step-by-step explanation:

Remember that  if  

I  =  Identity Matrix    

then    det(I)=1.

Also remember that for any invertible matrix  

A*A^{-1}  = I =Identity Matrix.

Therefore    

det(A*A^{-1})  = det(A)*det(A^{-1}) = det(I) = 1

Therefore  

 det(A)*det(A^{-1}) = 1      and         det(A^{-1}) = 1/det(A)

You might be interested in
Above is a table with missing terms. Come up with a possible common difference that makes sense and list the missing terms.
Rina8888 [55]

Answer:

common ratio:2 2. 18  3.36  4.72 equation: 4.5(2^x)

Step-by-step explanation:

144=2*2*2*2*3*3    9=3*3

the common ratio would be 2

2. 9*2=18

3. 18*2=36

4. 36*2=72

(check) 72*2=144

0. 9/2=4.5

equation: 4.5(2^x)

7 0
2 years ago
(6x+7) - (9x-5) HELP​
ycow [4]

Answer:-3x+12

Step-by-step explanation:

7 0
3 years ago
Read 2 more answers
BC = x + 14, AB = x + 10, AC = 22
irinina [24]

ab = x + 10 \\  bc = x  + 14 \\ ac = 22  \\ (x + 10) + (x + 14) = 22 \\ x + x + 10 + 14 = 22 \\ 2x + 24 = 22 \\ 2x = 22 - 24  \\ 2x =  - 2 \\ x =  \frac{ -2}{2}  \\ x =  - 1

4 0
2 years ago
What is the value of x in the equation 58 = 10x − 2?
solong [7]

Answer:

6

Step-by-step explanation:

10x6=60-2=58

7 0
3 years ago
Read 2 more answers
The unknown measures of one triangle are about:
olga_2 [115]
Answer: but I need the points sorri
8 0
3 years ago
Other questions:
  • Solve. x² + 20x + 100 = 50
    14·2 answers
  • (50 points + Brainliest for RIGHT answer).
    14·2 answers
  • What is the solution to the system of equation 2x-y=7<br> Y=2x+3
    11·1 answer
  • I need help with this problem.
    13·1 answer
  • 14 + 3х - 5 + 4х how do I solve ​
    6·2 answers
  • Is this relation a function?
    13·1 answer
  • Please press this link it is a free college tutoring website its useful just trying to look out for yall if you guys need help w
    7·1 answer
  • Whoever answers gets brainlist!
    13·1 answer
  • I need help fast the answers fro each question are in the drop down menu
    15·2 answers
  • G(n)=n^3+n<br> g(-3)<br> help!
    5·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!