# If A = <img

Given: To find: value of x and y

Given equation: A2 + xI = yA

Firstly, we find the A2   Putting the values in given equation

A2 + xI = yA    On Comparing, we get

16 + x = 3y …(i)

y = 8 …(ii)

56 = 7y …(iii)

32 + x = 5y …(iv)

Putting the value of y = 8 in eq. (i), we get

16 + x = 3(8)

16 + x = 24

x = 8

Hence, the value of x = 8 and y = 8

So, the given equation become A2 + 8I = 8A

Now, we have to find A-1

Finding A-1 using given equation

A2 + 8I = 8A

Post multiplying by A-1 both sides, we get

(A2 + 8I)A-1 = 8AA-1

A2.A-1 + 8I.A-1 = 8AA-1

A.(AA-1) + 8A-1 = 8I [AA-1 = I]

A(I) + 8A-1 = 8I

A + 8A-1 = 8I

8A-1 = – A + 8I     Ans. 𝒳 = 8, 𝒴 =8 and A-1 = . .

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