Let A and B be matrices of orders 3 × 2 and 2 × 4 respectively. Wri

1.	Let A and B be matrices of orders 3 × 2 and 2 × 4 respectively. Write the order of matrix AB.
Answer» We are given that, Order of matrix A = 3 × 2 Order of matrix B = 2 × 4 We need to find the order of matrix AB. We know that, Matrix A × Matrix B = Matrix AB If order of matrix A is (m × n) and order of matrix B is (r × s), Then, Matrices A and B can be multiplied if and only if n = r. That is, Number of columns in A = Number of rows in B Also, The order of resulting matrix AB comes out to be m × s. Applying it, Number of columns in A = 2 Number of rows in B = 2 This means, Matrices A and B can be multiplied, And its order will be given as : Order of matrix AB = 3 × 4 Thus, Order of matrix AB = 3 × 4

Let A and B be matrices of orders 3 × 2 and 2 × 4 respectively. Write the order of matrix AB.

Answer»

We are given that,

Order of matrix A = 3 × 2

Order of matrix B = 2 × 4

We need to find the order of matrix AB.

We know that,

Matrix A × Matrix B = Matrix AB

If order of matrix A is (m × n) and order of matrix B is (r × s),

Then,

Matrices A and B can be multiplied if and only if n = r.

That is,

Number of columns in A = Number of rows in B

Also,

The order of resulting matrix AB comes out to be m × s.

Applying it,

Number of columns in A = 2

Number of rows in B = 2

This means,

Matrices A and B can be multiplied,

And its order will be given as :

Order of matrix AB = 3 × 4

Thus,

Order of matrix AB = 3 × 4

Discussion

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