What is the relationship between matrix invertibility and matrix equal to zero in linear algebra?

What is the relationship between matrix invertibility and matrix equal to zero in linear algebra?

As the topic involves invertibility, so the matrix should be a square matrix
The necessary and sufficient condition for the invertibility of square matrix A is that the determinant | a | ≠ 0
Or rather
The necessary and sufficient condition for the irreversibility of matrix A is that the determinant | a | = 0

Linear Algebra: how much is the matrix (E + a) ∧ 100th power? How to calculate this kind of formula

Concrete analysis of specific problems
1 induction
2 into vector operations, such as α (β α) β α αβ
Using the properties of special matrix, such as diagonal matrix, etc

What does the quadratic form tr (a) mean in linear algebra

Is the trace of a matrix, the sum of all elements on the main diagonal

Add the plus sign, minus sign, multiplication sign and division sign in the blank of the following question: 9 8 7 6 5 4 3 2 1 = 1000

[9*8*7-(6+5-4-3)]*2*1=1000
Is there a line with brackets

In order to know that the equation (ab-2b) x square + 2 (B-A) x + 2A AB = 0 has two equal real roots, we can find the value of 1 / A + 1 / b
It seems that the answer is wrong

The result is 1
The method is as follows: the equation has two equal solutions satisfying the formula (bsquare - 4AB = 0). After simplification, it is 4A square + 8ab + 4B square - 8ab (a + b) + 4 (AB) square = 0
(2a + 2b-2ab) square = 0
So a + B = ab

Given that a set of data between X and Y is x0123y135-a7 + A, then the regression linear equation y = BX + a of Y and X must pass the fixed point ()
A. （4，32）B. （32，4a）C. （32，4）D. （6，16）

. x = 0 + 1 + 2 + 34 = 32,. Y = 1 + 3 + 5 − a + 7 + A4 = 4 ∵ regression linear equation must pass through the center of the sample, y = BX + a must pass through the fixed point (32,4), so select: C

Help me calculate a definite integral problem, very simple
Find, the graph enclosed by the curve y = x ^ 2, x = y ^ 2 revolves around the X axis and Y axis respectively, find the volume and area?
Give a detailed process, thank you

Area first:
S=∫[0--->1] (√x-x²) dx
=(2/3)x^(3/2)-(1/3)x³ |[0--->1]
=1/3
Obviously, the volume of the body of revolution around the x-axis is the same as that around the y-axis
V1=π∫[0--->1] (√x)² dx
=π∫[0--->1] x dx
=(π/2)x² |[0--->1]
=π/2
V2=π∫[0--->1] (x²)² dx
=π∫[0--->1] x⁴ dx
=(π/5)x⁵ |[0--->1]
=π/5
V=V1-V2=3π/10

It takes 15 minutes, 10 hours and 12 hours for a manuscript to be copied by Party A alone, Party B alone and Party C alone. What's the work efficiency ratio of Party A, Party B and Party C? If three people copy it together, how many hours will it take to finish it? If three people copy it two hours later, how many hours will it take for Party A, Party B and Party C to finish the rest? If Party A and Party C copy it three hours together, how many hours will it take for Party B and Party C to copy the rest?
For a project, Party A and Party B cooperate for 6 hours, Party B and Party C cooperate for 10 hours, and Party A and Party C cooperate for 7.5 hours?
(arithmetic within sixth grade of primary school)

For a manuscript, it takes 15 minutes for a person to copy it alone, 10 hours for B person to copy it alone, and 12 hours for C person to copy it alone. What is the work efficiency ratio of a, B, and C person? 15:10:12 if three people copy it together, how many hours will it take to copy it? 1 ÷ (1 / 15 + 1 / 10 + 1 / 12) = 1 ÷ 15 / 60 = 4 if three people copy it for two hours, how many hours will it take for a, B, and C person to copy it

It is known that the ellipse C takes F1 (- 2,0) F2 (2,0) as the focus and solves the elliptic equation (2) through P (- 5 / 2,3 / 2) (1) if the line L with the slope of 1 intersects the ellipse C at A.B
And the circle with diameter AB just passes through the midpoint of ellipse C to find the equation of line L

c = 2
x^2 / a^2 + y^2 / (a^2 - c^2) = 1
25/(4a^2) + 9/(4(a^2-c^2)) = 1
solve a = sqrt(10)
x^2/10 + y^2 / 6 = 1

To decimal point, multiplication and division! Each 99!

1. 3/7 × 49/9 - 4/3 2. 8/9 × 15/36 + 1/27 3. 12× 5/6 – 2/9 ×3 4. 8× 5/4 + 1/4 5. 6÷ 3/8 – 3/8 ÷6 6. 4/7 × 5/9 + 3/7 × 5/9 7. 5/2 -（ 3/2 + 4/5 ） 8. 7/8 + （ 1/8 + 1/9 ） 9. 9 × 5/6 + 5/6 ...