Question

If A is a square matrix such that A2=A, then write the value of 7A−(I+A)3 where I is an identity matrix.​

Answer 1

Answer:

given A2=A

7A−(I+A)3=7A−[I3+3A2I+3AI2+A3]

=7A−[I+3A+3A+A2.A]

=7A−[I+3A+3A+A]

=7A−I+7A

=−I

Answer 2

Answer:

7A-(1+A)^3=7A-(1^3+A^3+3×1^2×A+3×1×A^2)

7A-(1+A^3+3A+3A^2)

7A-(1+A×A+3A+3A×A)

7A-(1+A×A+3A+3A)

7A-(1+A^2+6A)

7A-(1+A+6A) (because A2=A

7A-(1+7A)

7A-1-7A

-1

so 7A-(1+A)^3=-1