Question

If A is a square matrix such that A^2=A find the value of 7A-(I+A)^3

Answer 1

Answer:

- I

Step-by-step explanation:

Given --->

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A is a square matrix and

A²=A

Find--->

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value of the

7A - (I + A) ³

solution ---->

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7A - ( I + A)³

we have a identity

(a+b)³=a³ + b³ + 3 a b ( a + b) applying it

=7A-{(I)³ +( A)³ + 3 I A(I + A)}

=7A-(I³ + A³ + 3 I²A + 3 I A²)

using A²=A

=7A-(I² I + A²A + 3 I A + 3 I A)

Using A²=A

=7A-(I .I + A A +3 A + 3A)

using A²= A

=7A-(I + A²+3 A +3A)

=7A-(I + A + 6A)

=7A - (I +7A)

=7A - I - 7A

=7A-7A - I

7A and (-7A) is equal to zero matrix

= 0 - I

= -I

where I is equal to identity matrix of same order as that of A

Additional information ---->

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(1).identity matrix is scalar matrix which has identity as a element in its main diagonal

(2). it is represented by I

(3). I. I=I and I. A=A

Answer 2

Answer:

Step-by-step explanation:

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