State, whether the following statements are true or false. If false, give a reason.

(i) If A and B are two matrices of orders 3 × 2 and 2 × 3 respectively; then their sum A + B is possible.

(ii) The matrices A_{2 × 3} and B_{2 × 3} are conformable for subtraction.

(iii) Transpose of a 2 × 1 matrix is a 2 × 1 matrix.

(iv) Transpose of a square matrix is a square matrix.

(v) A column matrix has many columns and only one row.

(i) False

Reason — For addition the order of both the matrices must be same.

Here, A and B have different orders.

Hence, the statement is false because the orders of both matrices are different.

(ii) True

Reason — For subtraction the order of both the matrices must be same.

Here, A and B have same orders.

Hence, the statement is true.

(iii) False

Reason — On transposing, the no. of rows and columns gets interchanged.

Hence, transpose of a 2 × 1 matrix will be of order 1 × 2.

Hence, the statement is false.

(iv) True

Reason — The transpose of a square matrix is also a square matrix.

Hence, the statement is true.

(v) False

Reason — A column matrix has only one column and can have many rows.

Hence, the statement is false.