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AP EAMCET20227 Jul 2022Morning ShiftMathematicsMatricesActual

Let A= [ array lll n & 0 & 0 0 & n & 0 0 & 0 & n array ] and B= [ array lll 0 & 0 & n 0 & n & 0 n & 0 & 0 array ] . Then, A^2+B^2+A B=

Options

  1. An(n l+n B+B)
  2. Bn(2 n l+B)
  3. Cn^2(2 l+B)
  4. Dn(n l+n A+B)

Correct answer

B. n(2 n l+B)

Step-by-step solution

A^2= [ array ccc n^2 & 0 & 0 0 & n^2 & 0 0 & 0 & n^2 array ], B^2= [ array ccc n^2 & 0 & 0 0 & n^2 & 0 0 & 0 & n^2 array ]A B= [ array ccc 0 & 0 & n^2 0 & n^2 & 0 n^2 & 0 & 0 array ] Now, A^2+B^2+A B aligned & =2 [ array ccc n^2 & 0 & 0 0 & n^2 & 0 0 & 0 & n^2 array ]+ [ array ccc 0 & 0 & n^2 0 & n^2 & 0 n^2 & 0 & 0 array ] & =2 n^2 [ array lll 1 & 0 & 0 0 & 1 & 0 0 & 0 & 1 array ]+n [ array lll 0 & 0 & n 0 & n & 0 n & 0 & 0 array ] & =2 n^2 I+n B=n(2 n I+B) aligned

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