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

Q: TRUE or FALSE: If A, B, C are square matrices such that CA = CB, then A = B. TRUE FALSE

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Q: Find two 3 x 3 matrices A and B such that det(A + B) + det(A) + det(B)

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Q: Let A, B be  matrices of the same order. Then det(A+B)=det(A) + det(B).  True or false

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Q: Let A and B be two square matrices. Which of the following statement or statements are always…

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Q: Show that A and B are not similar matrices

A: Given matrix is The characteristic polynomial of matrix A is

Q: Let A and B be two square matrices of the same size. Prove that det(AB) = det(BA).

A: Using Determinant and elementary row operations,

Q: Suppose that  |A| + |B| = |A + B| , find a 2x2 matrix for A and B

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Q: find A*B and B*A for the matrices A= 10 1 2 1 1 3 2 -1 B= 0 0 3 1 2 4 -1 -1 0

A: We have to find AB and BA for the matrices                                             A=10121132-1…

Q: Let A and B be 3 × 3 matrices such that det (B) = -2 and 27 = det (-3AB A" B ²). 2 Find det(A).…

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Q: O True

A: True

Q: Let. A=[3,2,1;4,2,3;-2,1,-3] Convert the matrix unit using elementary operations

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Q: 3. Give an example of two 2 × 2 matrices A and B for which (AB)² # A²B².

A: To prove above equation with an example

Q: Let A and B be similar matrices Show that if A? = A then B = B.

A: Two matrices C and D are said to be similar matrices if there exists a non-singular matrix P such…

Q: Let A and B be square matrices of the same size. (a) Prove that if A and B are both diagonal, then…

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Q: -() --()-() 3 6 3 3 1 2 1 2 1 1 2 1 3 1 2 3 2 2 A = 3 1 2 В C = 4 4 3 4 4 3

A: Claim: We have to find E such that EA=Bi.e. E=BA-1 And F such that, FA=C i.e. F=CA-1 A=121312443then…

Q: (1) Let A and B be two 2 × 2 matrices. Does det(A – B) = det(A) – det(B), explain your answer.

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Q: If A and B are square matrices of the same order, then (AB)T = AT BT True False

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Q: If A is a 3 x3 matrix and det(A) =-3, what is det(4A)?

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Q: Find the rank of the following matrices: 1 2 2 3 3 2 1 тank(A)— 2 3 таnk(A)—

A: We use the definition of the rank of a matrix to find the rank of given matrices.

Q: Let A and B be square matrices of order 3 such that |A-| = x + 7 with x + -7 and |A * A" | = . What…

A: A and B are square matrices. Therefore, det(AB)=det(A).det(B) det(A)=det((A)T) We will use these…

Q: If A and B are nXn matrices, then (A-B) =A-2AB+B Select one:

A: A-B2=A-BA-B=A2-AB-BA+B2

Q: (8) Let A and B be m x n matrices. Prove that the rank of A + B is less than or equal to the rank of…

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