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If (AB + B)T = BTX  then X is equal to ?

  1. AT
  2. AT + I
  3. BT + I
  4. BT
  5. I

Answer (Detailed Solution Below)

Option 2 : AT + I
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Detailed Solution

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Concept:

Transpose of a sum: The transpose of the sum of two matrices is equivalent to the sum of their transposes: (A + B)T = AT + BT

Transpose of a product: The transpose of the product of two matrices is equivalent to the product of their transposes in reversed order: (AB)T = BT AT

Calculation:

Given: (AB + B)T = BTX

⇒ (AB + B)T 

= (AB)T + BT

= BTAT + BTI

= BT (AT + I) = BT X

∴ X = (AT + I)

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