Question

Matrix \[A = \begin{bmatrix} x & y \end{bmatrix}\] and Matrix \[B = \begin{bmatrix} a \\ b \end{bmatrix}.\]

Assertion (A): Product BA is possible and order of resulting matrix is \[2 \times 2.\]

Reason (R): The product BA of two matrices A and B is possible only if number of rows in matrix B is same as number of columns in matrix A.

विकल्प

• A is true, R is false.

• A is false, R is true.

• Both A and R are true and R is the correct reason for A.

• Both A and R are true and R is the incorrect reason for A.

Answer 1

A is true, R is false.

Explanation:

∴ Order of matrix A = 1 × 2

∴ Order of matrix B = 2 × 1

Since product of matrix is possible, only when the number of columns in the first matrix is equal to number of rows in second.

Since,

Number of columns in B = 1

Number of rows in A = 1

∴ Product BA is possible.

We know that,

The no. of rows in the resulting matrix is equal to the no. of rows in first matrix and no. of columns equals to the no. of columns in second matrix.

∴ Order of matrix BA = 2 × 2

So, assertion is true. But reason says the product BA is possible only if number of rows in matrix B is same as number of columns in matrix A, which is false.