Let A be a non-singular square matrix such that A 2 = A satisfying Ι - 0.8 A - 1 = Ι - α A where Ι is a unit matrix of the same order as that of A , then the value of - 4 α is equal to

Question

Let A be a non-singular square matrix such that A 2 = A satisfying Ι - 0.8 A - 1 = Ι - α A where Ι is a unit matrix of the same order as that of A , then the value of - 4 α is equal to,

MARKS App · Accepted Answer

Ι - 0.8 A - 1 = Ι - α A Ι - 0.8 A Ι - 0.8 A - 1 = Ι - 0.8 A Ι - α A Ι = Ι - α + 4 5 A + 4 α 5 A 2 A α + 4 5 = 4 α 5 A ⇒ α 5 = - 4 5 ⇒ α = - 4

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