Let A be a 2 \\times2 real matrix with entries from \{0,1\} and | {A}| \\neq 0 . Consider the following twostatements: ( {P}) If {A}\neq{I}_{2}, then | {A}|=-1 (Q) If |{A }|=1, then {\tr}( {A})=2, where {I}_{2} denotes 2 \\times2 identity matrix and {\tr}( {A})denotes the sum of the diagonal entries of A. Then: [2 Sep 2020 Shift 1]

Correct Answer is : (P) is false and (Q) is true

Matrices and Determinants Part 1

Section: Mathematics

Question : 4 of 100

Marks: +1, -0

Let A be a 2×2 real matrix with entries from {0,1} and |A|≠0. Consider the following twostatements:
(P) If A≠I2, then |A|=−1
(Q) If |A|=1, then tr(A)=2,
where I2 denotes 2×2 identity matrix and tr(A)denotes the sum of the diagonal entries of A. Then:

[2 Sep 2020 Shift 1]

(P) is true and (Q) is false
Both (P) and (Q) are false
Both (P) and (Q) are true
(P) is false and (Q) is true

Validate

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