The following are true/false questions, please provide T or F so that I may chec

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The following are true/false questions, please provide T or F so that I may check my answers with what you provide. Thanks!


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.

P^{-1}=P^T

P^{17} (i.e., P to the power 17) is a permutation matrix.

P+Q is a permutation matrix.

If A is symmetric then A^{-1} = A^T.

The product of two symmetric matrices is symmetric.

If A is symmetric then it is invertible.

(AB)^T= A^TB^T.

(AB)^T= B^TA^T.

A^TA and AA^T are both symmetric.

A^TA = AA^T

If AB is invertible, then so are both A and B.

R^{200}=I.

If A and B are invertible, then so is AB and (AB)^{-1} = A^{-1}B^{-1}.

If A and B are invertible, then so is AB and (AB)^{-1} = B^{-1}A^{-1}.

AB=BA

If A and B are invertible then so is A+B.

IF A, B, and A+B are invertible then (A+B)^{-1} = A^{-1}+B^{-1}.

If A has a column of zeros then it cannot be invertible.

If A is not invertible it must have a row or a column of zeros.

If A is upper triangular and invertible then A^{-1} is upper triangular.

If B is the inverse of A^2 then AB is the inverse of A.

If AB is invertible then so is A and so is B.

Explanation / Answer

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