Q. Which of the following property of matrix multiplication is correct?

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Q. For a matrix A, if a matrix B is obtained by changing its rows into columns and column into rows, then relation between A and B is?

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Q. For matrix A, (Aᵀ)ᵀ is equals to ___________

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Q. For matrix A and a scalar k, (kA)ᵀ is equal to _________

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Q. If A is a lower triangular matrix then Aᵀ is a _________

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Q. If matrix A and B are symmetric and AB = BA iff _________

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Q. A matrix can be expressed as sum of symmetric and anti-symmetric matrices.

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Q. The determinant of a diagonal matrix is the product of leading diagonal’s element.

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Q. If for a square matrix A and B,null matrix O, (AB)ᵀ = O implies Aᵀ = O and Bᵀ = O.

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Q. Let A = [aᵢⱼ] given by abᵢⱼ = (i-j)³ is a _________

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Q. Trace of the matrix of odd ordered anti-symmetric matrix is _________

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Q. For a matrix A, B and identity matrix I, if a matrix AB=I=BA then?

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Q. For matrix A, (A₃) = I, A⁻¹ is equals to _________

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Q. Let A = [0 1 0 0 ], A⁻¹ is equal to _________

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Q. If A is an invertible square matrix then _________

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Q. If matrix A, B and C are invertible matrix of same order then (ABC)⁻¹ = _________

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Q. If A is non singular matrix then AB = AC implies B = C.

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Q. For a matrix A of order n, the det(adj(A)) = (det(A))ⁿ, where adj() is adjoint of matrix.

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Q. For a non-singular matrix A, A⁻¹ is equal to _________

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Q. Let I₃ be the Identity matrix of order 3 then (I₃)⁻¹ is equal to _________

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