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 )

Question

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 ), order of B T is 5 × 7, order of B T A is 7 × 7, order of B T A is 5 × 5, B T A is undefined

MARKS App · Accepted Answer

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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