Elementary Linear Algebra Test Questions and Answers

Elementary Linear Algebra Test Questions and Answers if A^2=I then A=I - Answer-F if AJ=A then J=I - Answer-F if A is square, then (A^T)^3 = (A^3)^T - Answer-T If A is symmetric, then I +A is symmetric. - Answer-T If AB = AC and A doesn't equal 0, then B = C. - Answer-F if A doesn't equal 0 then A^2 doesn't equal 0 - Answer-F if A has a row of zeros so also does BA for all B - Answer-F If A commutes with A+B then A commutes with B - Answer-T If B has a column of zeros so also does AB - Answer-T If AB has a column of zeros, so also does B. - Answer-F If A has a row of zeros, so also does AB. - Answer-T If AB has a row of zeros, so also does A. - Answer-F if A doesn't equal 0 is a square matrix then A is invertible - Answer-F if A and B are both invertible then A+B is invertible - Answer-F if A and B are both invertible then (A^-1B)^T is invertible - Answer-T if A^4=3I then A is invertible - Answer-T if A^2=A and A doesn't equal 0 then A is invertible - Answer-F if AB=B for some B doesn't equal 0 then A is invertible - Answer-F if A is invertible and skew symmetric (A^T = -A) the same is true of A^-1 - Answer-T if A^2 is invertible then A is invertible - Answer-T