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Let A and B be two matrices such that the order of A is 5 × 7 . If A T B and B A T are both defined, then (where A T is the transpose of matrix A )

Options

  1. Aorder of B T is 5 × 7
  2. Border of B T A is 7 × 7
  3. Corder of B T A is 5 × 5
  4. DB T A is undefined

Correct answer

B. order of B T A is 7 × 7

Step-by-step solution

Order of A is 5 × 7 ⇒ order of A T = 7 × 5 If A T B is defined ⇒ order of B must be 5 × n If B A T is defined ⇒ order of B must be m × 7 Hence, the order of B is 5 × 7 ⇒ Order of B T is 7 × 5 ⇒ Order of B T A is 7 × 7

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