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If matrix A = {bmatrix}2&-2-2&2{bmatrix} and A^2 = pA, then wr

Question

If matrix $A = [2 - 2 - 2 2]$ and $A^{2} = p A$ , then write the value of $p$ .

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Elijah Discussed

If matrix

A = [2 - 2 - 2 2]

and

A^{2} = p A

, then write the value of

p

10 mins ago

Discuss this question LIVE

10 mins ago

Text solutionVerified

A = (2 - 2 - 2 2)

then

A^{2}

can be computed as shown below:

A^{2} = (2 - 2 - 2 2) (2 - 2 - 2 2) = (2 \times 2 + - 2 \times - 2 - 2 \times 2 + 2 \times - 2 2 \times - 2 + (- 2) \times 2 - 2 \times - 2 + 2 \times 2)

implies

A^{2} = (8 - 8 - 8 8)

Since

A^{2} = p A

, therefore,

(8 - 8 - 8 8) = p (2 - 2 - 2 2)

(8 - 8 - 8 8) = (2 p - 2 p - 2 p 2 p)

Now equating the matrices we get

2 p = 8 ⟹ p = 4

Hence,

p = 4

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Question Text	If matrix $A = [2 - 2 - 2 2]$ and $A^{2} = p A$ , then write the value of $p$ .
Answer Type	Text solution:1
Upvotes	150