Assertion (A): The product of a row matrix and a column matrix is possible.
Reason (R): Two matrices of the same order can be multiplied.
Both A and R are true, and R is the correct explanation of A.
Both A and R are true, but R is not the correct explanation of A.
A is true, but R is false.
A is false, but R is true.
Answer
The product of a row matrix and a column matrix is possible.
A row matrix has order 1 × n and a column matrix has order m × 1.
If n = m, so the product is defined and gives a 1 × 1 matrix.
So, assertion (A) is true.
Two matrices of the same order cannot be multiplied.
If the matrix are of the same order and not square, example 2 × 3 and 2 × 3, then (2 × 3) × (2 × 3) is not defined because the number of columns of the first matrix is not equal to the number of rows of the second matrix.
So the statement “Two matrices of the same order can be multiplied” is false.
Reason (R) is false.
A is true, R is false.
Hence, option 3 is the correct option.
Assertion (A): A rectangular matrix can be a diagonal matrix.
Reason (R): A square matrix in which every non-diagonal element is 0 is called a diagonal matrix.
Both A and R are true, and R is the correct explanation of A.
Both A and R are true, but R is not the correct explanation of A.
A is true, but R is false.
A is false, but R is true.
Answer
In a rectangular matrix number of rows ≠ number of columns.
A diagonal matrix is defined only for square matrices, where all non-diagonal elements are 0 and diagonal elements may be nonzero.
Hence, a rectangular matrix can never be diagonal, because diagonal position exists only when rows = columns.
So, assertion (A) is false.
A square matrix in which every non-diagonal element is 0 is called a diagonal matrix.
This is the correct definition of a diagonal matrix.
So, reason (R) is true.
A is false, R is true.
Hence, option 4 is the correct option.
Assertion (A): For any two matrices A and B, A + B = B + A.
Reason (R): We can add only two matrices of same order.
Both A and R are true, and R is the correct explanation of A.
Both A and R are true, but R is not the correct explanation of A.
A is true, but R is false.
A is false, but R is true.
Answer
Matrix addition follows the commutative law — but only when A and B are of the same order.
If that is the condition, A + B = B + A always holds true.
So, Assertion (A) is true.
Matrix addition is defined only when both matrices have the same order.
So, Reason (R) is true.
Both A and R are true, but R is not the correct explanation of A.
Hence, option 2 is the correct option.
Assertion (A): For any two square matrices A and B of same order, AB and BA both exist.
Reason (R): For any two matrices A and B, the product AB exists only when number of rows in A = number of columns in B.
Both A and R are true, and R is the correct explanation of A.
Both A and R are true, but R is not the correct explanation of A.
A is true, but R is false.
A is false, but R is true.
Answer
If A and B are square matrices of the same order (say n × n), then :
Thus, for AB, no. of columns in A = no. of rows in B.
Thus, AB is possible.
For BA, no. of columns in B = no. of rows in A.
Thus, BA is possible.
Assertion (A) is true.
The rule for matrix multiplication is : AB exists if the number of columns of A = number of rows of B.
Reason (R) is false.
A is true, R is false.
Hence, option 3 is the correct option.
If A = and B =
Assertion (A): Product AB of the two matrices A and B is possible.
Reason (R): Number of columns of matrix A is equal to number of rows in matrix B.
Both A and R are true, and R is the correct explanation of A.
Both A and R are true, but R is not the correct explanation of A.
A is true, but R is false.
A is false, but R is true.
Answer
Order of matrix A = 1 × 2
Order of matrix B = 2 × 2
Since, no. of columns in A is equal to number of rows in B.
∴ AB is possible.
Both A and R are true, and R is the correct explanation of A.
Hence, option 1 is the correct option.