Which of the following subsets of R³×3 are subspaces of R³×³? A. The non-invertible 3 x 3 matrices B. The 3 x 3 matrices with trace 0 (the trace of a matrix is the sum of its diagonal entries) C. The invertible 3 x 3 matrices

Q: Let A be a m×n matrix. Prove that AB and Ba both exist only if B is an n×m matrix.

A: Explanation of the answer is as follows

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Q: Prove that the n × n identity matrix is orthogonal.

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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,

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A: The given matrices

Q: Suppose that the square matrix A is invertible. Show that the inverse of A is unique.

A: See below the explanation

Q: Determine the dimensions of Nul A and Col A for the matrices. A = 10

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A: Here, CA=I, where I is the identity matrix.

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Q: Determine the dimensions of Nul A and Col A for the matrices. A =

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A: As per our company guideline we are supposed to answer only one question kindly post remaining…

Q: Find a vector that spans the kernel of the following matrix: [ 1 0 2 4 ] [ 0 1 -3 -1 ] [ 3 4 -6 8 ]…

A: LET MATRIX IS A=1  0   2  40  1-3-13  4-6   80-1   3  4 NOW, THE KERNEL OF A DEFINED AS-:…