Test 1 and 2 linear algebra true or false

im cooked

For any two matrices A and B, it holds that A + B = B + A

True

For any two matrices A and B, it holds that AB = BA

False

If det(A) = 0, then the linear system Ax = b has no solution

False

Elementary row operation permit one equation in a linear system to be subtracted from another

True

det(A+B) = det(A) + det(B)

False

Every linearly independent subset of a vector space V is a basis for V

False

A set containing a single vector is linearly independent

True

Every orthonormal basis of a vector space is an orthogonal basis

True

Every nonzero vector space has an orthonormal basis

True

If lambda = 0 is an eigenvalue of A, then A is not invertible

True

Every square matrix has a Jordan Canonical form

true

a matrix is orthogonal if it has orthogonal columns

False

If two square matrices have the same characteristic polynomial, then they are similar

False

Two square matrices are similar if and only if they have the same Jordan Canonical form

True

If an n x n matrix A is diagonalizable, then the characteristic polynomial determines the Jordan Canonical form of A

True

For a matrix A, in the singular value decomposition A = UEV^T, the factor U satisfies UU^T = I

True

If A is invertible and o is a singular value of A, then 1/o is a singular value of A^-1

True

If A and B are similar square matrices, then all singular values of A and B are the same

False

There is a 2 × 3 real matrix A such that A^T A and A A^T are both invertible

False

If A is an m x n matrix and A has a QR factorization, then it must hold that m > n

False