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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 ______.
Options
2 × 2
3 × 3
2 × 3
3 × 2
MCQ
Fill in the Blanks
Solution
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
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