If A and B are (n × n) matrices, then e“ e = et eA". a) True b) False

Q: If the RREF of A|I is I| B, then AB is the identity matrix. A True B False

A: We have to check whether the given statement is true or false.

Q: 31. If A and B are n x n matrices, then the diagonal entries of the product matrix AB are…

A: Matrix multiplication is possible only when the number of columns of first matrix are equal to the…

Q: If A and B are 4×4 matrices, det(A)=−2, det(B)=−7, then

A:

Q: 5) Give an example of matrices D and F where DF is defined, but FD is not, and clearly explain why…

A:

Q: If A and B are nonsingularnxn matrices, then Select one: a. AB is nonsingular b. AB is singular

A: Given that A nad B are nonsingular n*n matrices.

Q: 3. Show that (AB)* B' A' by using the matrices A and B giver [8 -2 5] 1 -5] B = 7 0 -3 A =1 -4 3 6.…

A:

Q: Show that if A and B are two n × n matrices with the same diagonalizing matrix X, then AB = BA.

A:

Q: TRUE/FALSE Assume that all the given matrices are n × n. det(AB) = det(BA)

A:

Q: If A and B are (n x n) matrices, then e"e a) True b) False

A: Any expression written in the form of ex form is known as exponential form. Property of exponential…

Q: b) If P−¹AP and P-¹BP are both diagonal matrices, show that AB = BA.

A:

Q: A, B, C are 3 x 3 matrices with det(A) = -3, det(B) = -2, det(C) = 6. What is det(A² BC-1)?

A: Given A, B and C are 3×3 matrices. and A=-3,B=-2,C=6 Find the determinant of A2BC-1.

Q: 23. If A and B are matrices, then both AB and BA are defined if and only if A and B are square…

A: 23. For two matrices to be multiplied the n of the column in the first matrix must be equal to the…

Q: Suppose that A and B are matrices having n rows. Prove that M(A|B) = (MA|MB) for any m ×n matrix M.

A:

Q: If A is an n xn matrix then det(A)=Ddet(-A). Select one: O True O False

A: Introduction:- Statement -> if A is square matrix of order n X n, then det(kA) = kn det(A)

Q: Let A = {aj}, B = {bj}, and C = {cj} be n × n matrices. Show that (A + B)C = AC + BC.

A: We  first show that both the products are defined. we will use the fact that when A and B have same…

Q: If A is a 3 x 3 matrix and B is a 2 x 2 matrix, then Select one: True False det(A) # det(B).

A:

Q: If A, B, C are square matrices of the same size such that AB = A C, then for sure B = C. True False

A: See the solution below.

Q: If A and B are square matrices of the same size such that AB = BA, prove that (AB)2 = A2B2.  By…

A:

Q: If A and B are n x n symmetric matrices, then AB is symmetric. A True В False

A:

Q: A and B are matrices, then both AB and BA are defined if and only if A and B are square matrices.…

A: We have to check

Q: A, B, C are 3 x 3 matrices with det(A) = -3, det(B) = -2, det(C) = 6. What is det(A" A-1)?

A: Given that A,B and C are 3*3 matrices. To find det(A^TA^-1)

Q: A, B, C are 3 x 3 matrices with det(A) = -3, det(B) = -2, det(C) = 6. What is det[(-3)A]? O 27 81 -9…

A:

Q: 7. Give the two matrices, Г1 2 3] A = |1 1 2 and B= 0 1 2 [i 1 1] 2 1 2 3 1 2 (a) Find det A, det B,…

A: Hey, since there are multiple questions posted, we will answer first question. If you want any…

Q: Prove: If A and B are n × n diagonal matrices, then AB = BA.

A: If A and B are n × n diagonal matrices, then AB = BA.

Q: Let A and B be two 4 × 4 matrices with rank(A)<4. Then rank(A²B)<4. Select one: O True O False

A:

Q: If A and B are n x n symmetric matrices, then AB is symmetric. ... (A) True B) False

A:

Q: Use a counterexample to show that the statement is false. If A, B, and C are matrices and AC = BC,…

A:

Q: Let A, B and C be 3x3 matrices with det(A) = 7, det(B) = 5 and det(C)= 6 find det(det(A).B'.C)…

A: It is given that detA=7,detB=5,detC=6 detdetAB-1C=det7×1detBadjBC=det76adjBC It is known that…

Q: If AB=AC, where A, B, and C are matrices, then this implies that B=C. O True O False

A: A-1A = A A-1 = I  Where A-1 = Inverse of A               I = Identity matrix

Q: If AB + BA is defined, then A and B are square matrices of the same size. True False

A: Given AB + BA is defined.

Q: Find 2 × 2 matrices A and B such that AB = O but BA ≠ O.

A: To Find: 2 x 2 matrices A and B such that AB = O but BA is not equal to O Here O is a zero matrix…

Q: Show that if A and B are n × n matrices and N(A − B) = Rn then A = B.

A:

Q: If A is an n Xn matrix then det(A)=Ddet(-A). Select one: True False

A: Given Statement If A is an nxn matrix then det(A)=det(-A).

Q: Let A, B, and C be n X n matrices. If A ∽B and B ∽C, then A ∽ C

A:

Q: If A and B are similar, then there exists a matrix P such that BK = P-AKP. Use this fact to find B,…

A:

Q: If A and B are nxn matrices such that AB = BA , show that (AB) = A²B² .

A: Suppose A  and  B be n×n matrix  such that AB=BA

Q: If A ̸= 0 and AB=AC, where A, B, C are square matrices, then B=C.

A:

Q: are the two matrices Simi Siari? If So find B=P'AP 20 030 3 00 A=

A: The solution are next step

Q: If A, B, and C are square matrices of the same order such that AC = BC, then A = B. True False

A: Given AC = BC

Q: Let A, B, C be (4 × 4) matrices, such that = a, det(B) = b, det(C) = c, a, b, c E R. What is the…

A: The transpose of the matrix can be calculated by replacing the rows with the columns of the matrix.…

Q: Let A, B, and C be three matrices of the appropriate sizes. Then, the following holds. AB = AC and…

A:

Q: If A and B are nxn matrices, then (AB) 2=A?B? A) True B) False

A: Given statment is true for all the matrix which satisfies the commutative property otherwise…

Q: Let A be an n × n matrix and c a real number. Show that if cA = O , then c = 0 or A = O .

A: Given: A be an n × n matrix and c be a real number. To prove that: if cA=0 , then c=0 or A=0.

Q: If the RREF of All is I| B, then AB is the identity matrix. A) True B) False

A:

Q: Is it true or false? If A and B nxn matrices |A+B|=| A |+ | B| Birini seçin: O Doğru O Yanlış

A: we have to identify the following is true or false

Q: If A and B are nxn matrices, then (AB)²=A²B²_ A) True B) False

A: Solution

Q: If the RREF of A|I is I | B, then AB is the identity matrix. (A) True B) False

A: We are given the RREF of A|I is I|B, we have to find whether AB is identity matrix or not

Q: Consider a 2x2 matrices a  b c  d a,b,c,d are subsets of {1,2,3}. If you were to form a matrix at…

A: Each of a,b,c,d has 3 choices. So there are 34=81 possible matrices.A matrix will not have inverse…

Matrices

‘Matrices’ is the plural form of the word matrix, and it is basically a spreadsheet in the form of a box. In mathematics, various functions can be carried out with matrices. Generally, a matrix comes in the shape of a square or rectangle. The elements are distributed horizontally in the form of rows, and vertically in the form of columns.