The following are true\\false questions: Note: P and Q are permutation matrices

Question

The following are truealse questions:

Note: P and Q are permutation matrices and that R is a permutation matrix that interchanges two (otherwise unspecified) rows.

If A is symmetric and A=LU then L = U^T.

PQ=QP

R^{-1} = R

R^{15} = R

The inverse of an invertible symmetric matrix is symmetric.

A (square) matrix being invertible means the same as it being non-singular.

A n imes n matrix is invertible if and only if elimination, possibly including row interchanges, produces n non-zero pivots.

The inverse of an invertible matrix is invertible.

(AB)^{-1}= A^{-1}B^{-1}.

(AB)^{-1}= B^{-1}A^{-1}.

if A and B are invertible, then so is AB.

Explanation / Answer

F T T F F T F F T T F

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