Let A be a 2×2 matrix with real entries. Let I be the 2×2identity matrix. Denote by tr (A), the sum of diagonal entries of A. Assume that A2=I.Statement 1: If A=Iand A=−I, then det A=−1.Statement 2: If A=Iand A=−I, then tr(A)=0.
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(i) Find equation of line joining (1,2) and (3,6) using determinants(ii) Find equation of line joining (3,1) and (9,3) using determinants.
Let f(x)=1−x1+x . If A is matrix for which A3=O,thenf(A) is (a)I+A+A2 (b) I+2A+2A2
(c) I−A−A2 (d) none of these
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If both A−21IandA+21 are orthogonal matices, then (a)A is orthogonal (b)A is skew-symmetric matrix of even order (c)A2=43I
(d)none of these