Matrices & Determinants Question - None

Question

For any 3 × 3 matrix M, let |M| denote the determinant of M. Let
E =

[\begin{matrix} 1 & 2 & 3 \\ 2 & 3 & 4 \\ 8 & 13 & 18 \end{matrix})

, P =

[\begin{matrix} 1 & 0 & 0 \\ 0 & 0 & 1 \\ 0 & 1 & 0 \end{matrix})

and F =

[\begin{matrix} 1 & 3 & 2 \\ 1 & 3 & 2 \\ 2 & 4 & 3 \end{matrix})

.
If Q is a nonsingular matrix of order 3 × 3, then which of the following statements is (are) TRUE?

Accepted Answer

The matrix P is an elementary permutation matrix. Calculating P^2 gives the identity matrix I. Checking the relation F = PEP involves matrix multiplication. The determinant property |A+B| = |A|+|B| is generally false. The trace property Tr(A+B) = Tr(A) + Tr(B) and Tr(P^-1 EP) = Tr(E) are used to verify option (D).

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