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Sum of Binomial Coefficients of Even Numbered Terms

If A ≠ A2=I, ...

Question

If $A \neq A^{2} = I,$ then $| I + A | =$

A

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B

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C

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Solution

$A^{2} = I \Rightarrow A^{2} - I = O$
$\Rightarrow (A - I) (A + I) = O$
$\Rightarrow | A - I | | A + I | = 0$
Since $A \neq A^{2} = I \Rightarrow A \neq I$
$∴ | A + I | = 0$

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Similar questions

A^{2} - A + I = 0

, then the inverse of A is
(a) A⁻²
(b) A + I
(c) I − A
(d) A − I

A \neq A^{2} = I,

| I + A | =

Q. Assertion :Let

A

2 \times 2

matrix with real entries. Let

I

2 \times 2

identity matrix. Denote by

t r (A)

, the sum of diagonal entries of

A

A^{2} = I

.

A \neq I

A \neq - I

d e t (A) = - 1

A \neq I

A \neq - I

t r (A) \neq 0

.

If $A = [\begin{matrix} x & 1 1 & 0 \end{matrix}]$ and $A^{2}$ =I then x=__

2 \times 2

matrix with real entries. Let I be the

2 \times 2

identity matrix. Denote by tr(A), the sum of diagonal entries of

A

A^{2} =

I.
Statement-l: If

A \neq I

A \neq - I

det A = - 1

.
Statement-2: If

A \neq I

A \neq - I

t_{1} {A) \neq 0

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