- #1
Briane92
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1. a) Prove the following holds for A
A is a matrix [a b, c d]
I is identity matrix.
A^2 = (a+d)A-(ad-bc)I.
b) Assuming ad-bc not equal to 0, use a) to obtain an expression for A^-1.
I proved the first equation, but I'm not seeing where it relates to the inverse. I know that ad-bc is the determinate. At first I was going to write A^-1 in terms of a,d,b,c in a matrix but I realize that this was done in class and its asking for an equation similar to the first one.
I just want a couple of hints, because I'm stuck.
A is a matrix [a b, c d]
I is identity matrix.
A^2 = (a+d)A-(ad-bc)I.
b) Assuming ad-bc not equal to 0, use a) to obtain an expression for A^-1.
The Attempt at a Solution
I proved the first equation, but I'm not seeing where it relates to the inverse. I know that ad-bc is the determinate. At first I was going to write A^-1 in terms of a,d,b,c in a matrix but I realize that this was done in class and its asking for an equation similar to the first one.
I just want a couple of hints, because I'm stuck.