if a^n=0, then deta=0
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if det(ab)=0, then det(a)=0 or det(b) =0
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if det(a)=0, then det(ab)=0
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if a is an nxn matrix then rank a = n iff det a is not 0
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if matrix a has two identical rows then det(a)=0
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if a is nxn, then det(ca) = c^ndet(a)
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if a is row equivalent to b and b is row equivalent to c then a is row equivalent to c
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let a be an nxn matrix whose entries are all 1's then det(a-ni)=0
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an nxn matrix a is singular iff 0 is an eigenvalue of a
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if a = a^- 1, then det(a) = /-1
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if a is an nxn skew symmetric matrix then x^tax = o for all x in r^n
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proof: if det(a) != 0 and ab = ac, then b = c
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if a is nonsingular with a^2 = a, then det(a) = 1
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determinant of a matrix class 9
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if matrix b is obtained from interchanging two rows of matrix a, then det(b) = -det(a)
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corollary to an nxn matrix a is non singular iff rank (a) = n
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[proof] if n is odd, then det(a) = 0 for skew-symmetric matrix
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[proof] a is zero matrix if tr(aa^t) = 0
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det(a^t) = det(a)
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an nxn matrix a is non singular iff rank a = n