If A is any square matrix. Then det(A) = a) det(A-1) b) det(AT) c) – det(AT) d) 0

Q: For matrix A, B if A – B = O, where O is a null matrix then * A = B B = 0 A = 0

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Q: An nx n matrix A is invertible if and only if it is row equivalent to I. O True O False

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Q: Enter a 3 x 3 symmetric matrix A that has entries a11 = 0, a2 = 2, a33 = 5, a21 = 3, a31 = 4, and…

A: a symmetric matrix is a square matrix that is equal to its transpose.

Q: An identity matrix is represented by. . O a. H-H O b. HH-H HH-1

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Q: If A is a square matrix such that A2 = 0, then A is invertible. True or false

A: A is a square matrix, so, det(AB) = det(A) det(B)

Q: Let a be a real number, and consider the matrix a 2 1 1 6 3 A =

A: Given:

Q: Demonstrate that A A-1 = A-1 A = I

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Q: Show that if A is a square matrix that satisfies the equation A2 -2A +I= 0, then A-1 = 2I -A.

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Q: If A can be row reduced to the identity matrix, then A is not invertible. True False

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Q: Let a matrix '2 -2 1 A 2 3 1 1 -2 - 2 2 Show that A"A = I and deduce that AT = A-1.

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Q: If A is an invertible matrix. Then det(AA-): 1D

A: IA is an invertible matrix To find det(AA-1)

Q: Suppose A is a 5 x 5 matrix for which det(A) = -3. What is the value of det(2A)? det(2A) =

A: Sol:- Given :- Det(A) = -3 and Dimension of 5 * 5 Matrix

Q: If A is a nonzero matrix of the form P, then Rank(A) = 2. а

A: Let A be a n×n matrix . If Determinant of A is not ZERO, Then   Rank(A)=n

Q: Find a 3 x 3 matrix A such that 1 -5 A 3 A 1 -3 and -2 A 4 1 -5 A = 3. ||

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Q: If A is an nxn invertible matrix, then det(A-1) is equal to O det (A)-"det(adj(A)) O None of these…

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Q: A matrix A is similar to matrix B, if f invertible matrix P, B = P'AP. Prove is similar to B and B…

A: Given that: A is similar to B such that: B=P-1.AP.

Q: If A and B are square matrices of the same size, then it is always the case that AB=BA.

A: Disclaimer: “Since you have asked multiple questions, we will solve the first question for you. If…

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 square matrix whose diagonal entries are all zero, then detA = 0.

A: Given information: A is a square matrix whose diagonal entries are all zero.

Q: 4. Find the symmetric matrix, diagonal form of the quadratic form Q = 2x? + 2y2 + 2z2 - 2xy- 2xz -…

A: The objective is to find the symmetric matrix and diagonal form of the quadratic form…

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

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Q: 22. If the order of matrix A is m x p. And the order of B is p x n. Then the order of matrix AB is?…

A: The order of Matrix A : m * p The order of Matrix B : p * n To find matrix AB  Multiply both…

Q: FInd the Solution by Considering Attachment.

A: The method of mathematical induction can be followed to prove above result. Now, The given matrix is…

Q: Enter a 3 x 3 symmetric matrix A that has entries a1 = 1, a2 = 5, a33 = 4, a12 = 0, a31 = 3, and a A…

A: A square matrix A is called a symmetric matrix if A=AT, i.e. a matrix is equal to it's transpose If…

Q: If A is a square matrix such that A =1, then A'is equal

A: Given, A is a square matrix such that A2=I.

Q: If A is a square Matrix such that A'-A, what are the possible values of det A?

A: Determinant possible values

Q: Are the two matrices similar? If so, find a matrix P such that B = P-'AP. (If not possible, enter…

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Q: If A is 3 x 3 matrix such that 1 -3 1 1 A 1 -3 Al 1 A 1 1 -3 -2 -4 then A is diagonalizable. Select…

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Q: Let A, B, and C be invertible matrices. Then (4A-1B"C²)-1 is equal to c--(B")-1A equal to the above…

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Q: Suppose A is a matrix that is 0 0 0 0 0 0 0 0 0 What is I-A

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Q: (a) The matrix ( (AB)-1 )T comes from (A-1 )T and (B-1 )T In what order?(b) If U is upper triangular…

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Q: 3 2 2 3 1, find the matrix B Such that AB = 5 3 4 3 4 2 1 6 1 5 6 4 , If A = 1

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Q: If A is a matrix such that

A: Given:  A-1=12-1-324 To determine: The value of matrix A.

Q: 4. A matrix A is similar to matrix B, if for some invertible matrix P, B = P'AP. Is B similar to A?

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Q: If A is a square matrix such that A = A1, then A must be equal to either the identity matrix I or…

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Q: If AT = A-1, where A is a real matrix, then A is

A: When transpose of A equal inverse of A , then A is

Q: Show that if A is a square matrix that satisfies the equation A2 - 2A + I = O, then A-1 = 2I - A.

A: Given that,                    A2-2A+I=0

Q: If A is an orthogonal matrix, then det(A) = ±1.

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Q: B: find A of the matrix 2 1 3 3 2 -1 -4 3 -1

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Q: If A + 0 and B+ 0 are square matrices of the same order, then AB + 0.

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Q: If A is a square matrix such that A3 = O, show that (I-A)~l = I + A + A2.

A: To prove that (I-A)~l = I + A + A2 If A is a square matrix such that A3 = O

Q: 2] find 1 -1 3 - If A = and B 1 |3| -2 (а) ЗА — В. - (b) The matrix X such that 3A – B+ 3X = 0. ||…

A: As per guideline we have to solve only three parts

Q: Consider the matrix A = 0 o 0 0 -2

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Q: If 4 [a] is a 3x3 matrix, such that ay i (2m-j) then the diagonal elements are

A:

Q: An n x n matrix A is invertible if and only if it is row equivalent to I. O True False

A: Given statement is "An n×n matrix A is invertible if and only if it is row equivalent to In."

Q: Let -1 1 A = -1 1 -1 -3 3 Find an upper triangular matrix which is orthogonally similar to A.

A: An upper triangular matrix is a triangular matrix with all elements equal to below the main…

Q: If A, B, and C are n x n invertible matrices, does the equation C-1(A + X)B¬ = In have a solution,…

A: Given A, B and C are n×n invertible matrices.

Q: If A is a 2 x 2 skew symmetric matrix, must det(A) = 0?

A: we have a 2×2 skew symmetric matrix.

Q: Are the two matrices similar? If so, find a matrix P such that B = P-!AP. (If not possible, enter…

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Q: 1) Find a diagonal matrix A that satisfies A-2 20,

A: Here, we need to find a diagonal matrix A such that A-2=2004