Determinant of matrix transpose = determinant of matrix itself? Thx!

Determinant of matrix transpose = determinant of matrix itself? Thx!

Yeah
According to the sixth article of determinant nature: row and column exchange, determinant unchanged
The transpose of matrix is just row column interchange

Let matrix A and B be square matrices, the value of determinant A is 5, and the value of determinant B is negative 3. Find the value of the transpose of determinant a multiplied by B
Given the value of determinant, how to find the value of transposed determinant

The value of a determinant is equal to the value of its transposed determinant. This problem is equal to the value of a transposed determinant multiplied by the value of B determinant, which is equal to the value of a determinant multiplied by B determinant, which is equal to 5 times 3,15

Given the value of determinant of matrix A is | a |, find the value of | a * |?

Because: A ^ - 1 = a * / | a|
So: a * = | a ＾ - 1
So: a × = a ＾ a ＾ - 1 = a ＾ n ＾ a ＾ - 1
And AA ^ - 1 = 1
So: | a | a ^ - 1 | = 1
So: | a ^ - 1 | = 1 / | a|
So: | a * | = | a | ^ n / | a | = | a | ^ (n-1)

Under what condition, the determinant of matrix a multiplied by B is equal to the determinant of matrix a multiplied by the determinant of matrix B,

First of all, we must ensure that a * B is a square matrix, which requires the number of rows (columns) of a = the number of columns (rows) of B
When a and B are square matrices of the same order, the proposition holds
When a and B are of different orders, if the column of a is more than the row of a, then the determinant of a * B is zero
If the columns of a are less than the rows of a, let the number of columns of a be n, then the determinant of a * B is equal to "the determinant of n-order submatrix of a * B corresponds to the determinant of n-order submatrix of a". Take all possible n-order submatrix of a in quotation marks and add them up (sigma)

Expand the following functions into power series of X and find the interval of the expansion
 

3）
Original formula = x / (1-x) (1 + 2x) = 1 / 3 [1 / (1-x) - 1 / (1 + 2x)]
=1/3[(1+x+x^2+...)-(1-2x+4x^2-8x^3+..)]
=1/3[3x-3x^2+9x^3+.+(1-(-1)^n*2^n)x^n+...]
The convergence domain is | X|

For the first day of junior high school, there are 20 problems in calculation and factorization,

Only the title
1、y^2-2y-x^2+1
2、(3a+2b)^2-2(3a+2b)(2b-3a)+(3a-2b)^2
3、 -m^3n^3+4m^2n^2-mn
4、 (x+1)(x+3)(x+5)(x+7)+15
5、 x^2-2xy+y^2-13x+13y+30
6、 4(x+2z)(x-2z)+12xy+9y^2
7、 a^4+(a+b)^4+b^4
8、 6x^2-7xy-3y^2-x+7y-2
9、 x^2+x-2
10、x^2-4xy+3y^2-x-y-2
11、x^2+3x-(a^2+a-2)
12、(2x+y)^2-(x+2y)^2
13、（m+n)^2-n^2
14、169(a-b)^2-196(a-b)^2
15、(a+b+c)^2-(a-b-c)^2
16、4(2p+3q)^2-(3p-q)^2
17、3ax^2-3ay^4
18、8y^4-2y^2
19、a＾2-10ab+25b＾2-5a+25b-6
20、x＾2+2xy+y＾2-x-y+1/4
21、a＾2-6ab+9b＾2-4a+12b+4
22、x＾3+2x＾2-5x-6
23、x＾2-xy-2y＾2-x-y
24、0.5(m+1)^2+2(m+1)(1-m)+2(m-1)^2
25、4xy^2-4x^2y-y^3
26、(4a^2 +1)^2 -16a^2
27、5^2008-7*5^2007+10^2006+2008
28、a^4+b^4-2a^2b^2
29、x(a-x)(a-y)-y(x-a)(y-a)

Given the function y = f (x) defined on (negative infinity, positive infinity), when x ∈ (0, positive infinity), f (x) = x (1 + 2 x power)
(1) If the function f (x) is an odd function, when x ∈ (negative infinity, 0), find the analytic expression of the function y = f (x)
(2) If the function y = f (x) is an even function, when x ∈ (negative infinity, 0), find the analytic expression of the function y = f (x)

(1) If the function f (x) is an odd function, when x ∈ (negative infinity, 0), find the analytic expression of the function y = f (x)
If x0, then f (- x) = - x (1 + 2 ^ (- x))
If it is an odd function, then f (- x) = - f (x)
So when x

Given that a and B are reciprocal to each other, the calculation result of A10 △ 5b is___ ．

Given that the difference between the square of polynomial 2x + my-12 and the square of polynomial NX - 3Y + 6 does not contain x, y, find the value of M + N + Mn

According to the meaning of the title:
2-n=0
m+3=0
The solution is: M = - 3, n = 2
M = - 3 and N = 2 generations, M + N + Mn = - 3 + 2-6 = - 7
So the value of M + N + Mn is - 7

Write some poems about wine

A glass of wine, sunshine in the west, no old friends
Singing in the daytime, drinking in the company of youth, returning home
The Chinese Army's return of wine, huqin, Pipa and Qiang flute
Ten thousand wine in a golden bottle and ten thousand delicacies on a jade plate
On the night of Spring River and Autumn Moon, the wine is often drunk alone
To listen to your song today, I'll take the spirit of drinking wine for a while
A cup of wine in a scattered place, a long life for the host and the guests
The spring wine is warm and the candle is red. Li Shangyin's Untitled
Open the shop and talk about mulberry and hemp with wine
Don't laugh at the mellow farm wine, but let the guests stay in the rich year
A cup of turbid wine, a thousand li home, Yan Ran not le, no plan to return. -- Fan Zhongyan's the pride of the fisherman
Water tune several sound, hold wine to listen, afternoon drunk wake up worry not wake up
Holding wine to the setting sun for you, and leaving evening photos among the flowers
After a dream, the tower is locked high, and the curtain is hung low when sobered up
When will the moon come, ask the sky with wine
Where do you wake up from drinking tonight? The willow shore, the breeze and the moon
Three glasses of two light wines, how can he be defeated by the wind when he comes late? -- Li Qingzhao's slow voice