Matrices — Class 12 Maths Solution

ncert misc SA NCERT,Misc,Q.No.15,Page.101
Question

If A is a square matrix such that $A^2 = A$, then ${(I + A)^3} - 7A$is equal to

  • (a) A
  • (b) $I - A$
  • (c) I
  • (d) 3A
Step-by-step Solution

.:

Option c is correct

We have $A^2 = A$

Now, ${(I + A)^3} - 7A = {I^3} + {A^3} + 3IA(I + A) - 7A$

$= I + {A^2} + 3A(I + A) - 7A = I + {A^2} + 3A + 3{A^2} - 7A$

$= I + 4{A^2} - 4A = I + 4A - 4A = I$

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NCERT & Exemplar solution for CBSE Class 12 Mathematics, Matrices. Curated by Sachin Sharma. Free for all students.