Let the rows of A ∈ Mn×n(F) be a1, a2, . . . , an, and let B be the matrix in which the rows are an, an−1, . . . , a1. Calculate det(B) in terms of det(A).

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: Find the projection matrix P, and the projection of b= (1,2,3) onto 2. Let A= -1 -1 the column space…

A: Given matrix is A=1001-1-1

Q: let Q(x)= x12 -8x1x2 -5x22 , then matrix A of the quadratic from is A=?

A: Explanation is given below..

Q: Suppose that A and B are invertible 2 x 2 matrices such that det(AT) = 2 and det(B) = -2. Let x ER…

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Q: Show that if B is a scalar multiple of the 2 × 2 identity matrix, then AB=BA for all 2 × 2 matrices…

A: Prove the following

Q: Find the meet of the zero-one matrices A and B if A=⎛⎝⎜110010101⎞⎠⎟ and B=⎛⎝⎜011100111⎞⎠⎟.

A: MUST KNOW: In a zero -one matrix all elements are either 0 or 1 and represent false and true…