Q8Multiple correct3 Marks31 Aug 2025

Consider the following sets. v_1(2) = { A in M_{2x2}(R) | A^T A = v_2 } and v_2(2) = { A in M_{2x2}(R) | A A^T = v_2 } Choose all the correct options from the following.

A

If A in v_1(2), then the rows of A are orthonormal but the columns need not be orthonormal.

B

If A in v_2(2), then the columns of A are orthonormal but the rows need not be orthonormal.

C

If A in v_1(2) and B in v_2(2), then $\text{det}(A) \text{det}(B)$ = +-1.

D

If A in v_1(2) and B in v_2(2), then A and B are equivalent.

E

If A in v_1(2) and B in v_1(2), then for any u in $\mathbb{R}^2$, ||Au|| = ||Bu|| where ||.|| represents the usual norm in $\mathbb{R}^2$.