10 Question MCQ (including Assertion)

If A and B are square matrices of order m such that \(\mathrm{A}^2-\mathrm{B}^2=(\mathrm{A}-\mathrm{B})(\mathrm{A}+\mathrm{B})\), then which of the following is always correct?

Which of the following can be both a symmetric and skew-symmetric matrix?

Four friends Abhay, Bina, Chhaya and Devesh were asked to simplify \(4 \mathrm{AB}+3(\mathrm{AB}+\mathrm{BA})-4 \mathrm{BA}\), where A and B are both matrices of order \(2 \times 2\). It is known that \(A \neq B \neq I\) and \(A^{-1} \neq B\).
Their answers are given as :
Abhay : 6 AB
Bina : \(7 \mathrm{AB}-\mathrm{BA}\)
Chhaya: 8 AB
Devesh : 7 BA - AB
Who answered it correctly?

If A and B are square matrices of same order, then \(\left(\mathrm{AB}^{\mathrm{T}}-\mathrm{BA}^{\mathrm{T}}\right)\) is a

If A and B are skew-symmetric matrices of same order, then \(\mathrm{AB}^{\prime}+\mathrm{BA}^{\prime}\) is a/an :

If \(\mathrm{A}^{2}=4 \mathrm{~A}+3 \mathrm{I}\) and \(\mathrm{A}^{-1}=\mathrm{xA}+\mathrm{yI}\), then the value of \((\mathrm{x}+\mathrm{y})\) is :

For any square matrix A , (A \(-\mathrm{A}^{\prime}\) ) is always

If a square matrix A is such that \(\mathrm{A}^{2}=\mathrm{A}\) and \((\mathrm{I}-\mathrm{A})^{3}=\mathrm{xA}+\mathrm{I}\), then value of \(x\) must be :

If \(A=\left[a_{i j}\right]\) is an identity matrix, then which of the following is true ?