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
Differentiate f(x)= square root of x times sin x
zysi [14]
Hello,

y= \sqrt{ x*sin(x) } \\

y'= \dfrac{sin(x)+x*cos(x)}{2 \sqrt{x*sin(x)} }
3 0
3 years ago
Read 2 more answers
Should the Supreme Court uphold or strike down DACA? Explain.
frez [133]

Answer:

The supreme court should up hold DACA.

Step-by-step explanation:

I don't know much about the issue but that DACA is bacicly the way for immigrants to come to the US legally. it is unconstitutional in the US to not. let immigrants have a way to enter the US in in a legal way.

5 0
2 years ago
Use a calculator to find the
Tamiku [17]
Use the calculator to find the Product
8 0
3 years ago
Um help. I have no clue what to do​
Arlecino [84]

I’m not sure but I think it’s sample x

5 0
3 years ago
Find the value of x.<br> 6<br> 14<br> 8<br> 0<br> 21<br> x = [ ? ]<br> 3x-12
love history [14]

Answer: 7

Step-by-step explanation:

By the angle bisector theorem,

\frac{21}{14}=\frac{3x-12}{6}\\21(6)=14(3x-12)\\126=14(3x-12)\\9=3x-12\\21=3x\\x=\boxed{7}

4 0
2 years ago
Other questions:
  • I need help, Please hurry, It's timed.
    7·2 answers
  • Find the slope of a line through a pair of points (2,-3) and (8,4)
    9·1 answer
  • Which point is not on the graph of the function y = x + 5?
    12·1 answer
  • Can someone help me out with this
    10·2 answers
  • f(x) = -4x^2+12x-9f(x)=−4x 2 +12x−9f, left parenthesis, x, right parenthesis, equals, minus, 4, x, squared, plus, 12, x, minus,
    11·1 answer
  • Draw to explain how you would make a ten to find 5+8.
    10·1 answer
  • UDD Question 6 10 pts Solve for x. Round to the nearest tenth (one decimal place). Just type the number, no unit of measurement.
    6·1 answer
  • Who else is watching the unas annus livestream<br><br>#Wearehere​
    10·2 answers
  • Please help due in 10 minutes
    12·2 answers
  • In triangle A B D , the measure of angle A is 10 degree less than the measure of angle B . The measure of angle D is 20 degree m
    7·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!