Question

The product of matrix P and Q is equal to a diagonal matrix. If the order of matrix Q is 3 × 2, then order of matrix P is ______.

विकल्प

• 2 × 2

• 3 × 3

• 2 × 3

• 3 × 2

Answer 1

The product of matrix P and Q is equal to a diagonal matrix. If the order of matrix Q is 3 × 2, then order of matrix P is 2 × 3.

Explanation:

Considering that Matrix Q has an order of 3 × 2. It indicates that Q has 2 columns and 3 rows.
The number of columns in P must equal the number of rows in Q for the product PQ to produce a diagonal matrix.

Since Q has 3 rows, P must have 3 columns.

Therefore, P has an order of n × 3m, where n is the number of rows in P. 

n = 2

then the order of P = 2 × 3