Q. For a skew symmetric even ordered matrix A of integers, which of the following will not hold true?

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Q. For a skew symmetric odd ordered matrix A of integers, which of the following will hold true?

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Q. Let A = [kaᵢⱼ]ₙₓₙ, B = [aᵢⱼ]ₙₓₙ, be an nxn matrices and k be a scalar then det(A) is equal to _________

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Q. The Inverse exist only for non-singular matrices.

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Q. If for a square matrix A and B, null matrix O, AB = O implies BA=O.

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Q. If for a square matrix A and B,null matrix O, AB = O implies A=O and B=O.

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Q. Let A be a nilpotent matrix of order n then?

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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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