Identity Matrix

Q. If A is a $3\times 3$ non-singular matrix such that $A{A}^{\prime }=A^{\prime }A$ and $B=A^{-1}{A}^{\prime }$ then BB' equals

1. I + B
2. I
3. $B^{-1}$
4. $\left(B^{-1}\right)$

Q. For a square matrix $A,$ if $A^3=O,$ then $I+A+A^2$ is equal to

1. $I+A$
2. $(I+A{)}^{-1}$
3. $I-A$
4. $(I-A{)}^{-1}$

Q. Choose the correct answer

1. Every identity matrix is a scalar matrix
2. Every scalar matrix is an identity matrix
3. Every diagonal matrix is an identity matrix
4. A square matrix whose each element is 1 is an identity matrix