Manipal MET2021MathematicsMatrices

If A= [ array ccc 1 & 0 & 0 0 & 1 & 0 a & b & -1 array ] , then A^2 is equal to

Options

Aunit matrix
Bnull matrix
CA
D-A

Correct answer

A. unit matrix

Step-by-step solution

Given, A= [ array rrr 1 & 0 & 0 0 & 1 & 0 a & b & -1 array ] aligned A^2 & =A A= [ array rrr 1 & 0 & 0 0 & 1 & 0 a & b & -1 array ] [ array rrr 1 & 0 & 0 0 & 1 & 0 a & b & -1 array ] & = [ array ccc 1 & 0 & 0 0 & 1 & 0 a-a & b-b & 1 array ]= [ array lll 1 & 0 & 0 0 & 1 & 0 0 & 0 & 1 array ] aligned

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