Consider the following statements:
(A) Two matrices of different orders can be equal.
(B) If \(\begin{bmatrix}x&2y\end{bmatrix} = \begin{bmatrix}3&8\end{bmatrix}\), then \(x = 3\) and \(y = 4\).
(C) A matrix of order \(2 \times 3\) can be equal to its transpose.
(D) If \(A = B\), then \(A' = B'\).
Choose the correct answer from the options given below:
Answer & explanation
Correct answer: option 4
The correct answer is Option (4) → (B) and (D) only
Two matrices are equal when they are of the same order and their corresponding elements are equal.
So matrices of different orders are never equal, and equal matrices have equal elements in every position.
Checking the statements
(A) Two matrices of different orders can be equal. — Incorrect. Equal matrices must have the same order.
(B) If \(\begin{bmatrix}x&2y\end{bmatrix} = \begin{bmatrix}3&8\end{bmatrix}\), then \(x = 3\) and \(y = 4\). — Correct. \(x = 3\) and \(2y = 8\), so \(y = 4\).
(C) A matrix of order \(2 \times 3\) can be equal to its transpose. — Incorrect. Its transpose is of order \(3 \times 2\), a different order.
(D) If \(A = B\), then \(A' = B'\). — Correct. \(A'\) and \(B'\) have the same order and the same element \(a_{ji} = b_{ji}\) in each position.