GATE | Sudo GATE 2020 Mock I (27 December 2019) | Question 16

The transpose of a matrix is the operation of switching rows and columns. Let r be a real number and A and B be matrices. Then, which of the following property does not hold ?

I. (AT)T = A
II. (A + B)T = BT + AT

III. (AB)T = BTAT

IV. (rA)T = rAT
(A) Only II
(B) Both II and IV
(C) None
(D) All


Answer: (C)

Explanation: I. (AT)T = A
II. (A + B)T = AT + BT = BT + AT
III. (AB)T = BTAT
IV. (rA)T = rAT

All given properties hold.

Option (C) is correct.

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