PQ=kI∣P∣.∣Q∣=k3
⇒∣P∣=2k=0⇒P is an invertible matrix
∵PQ=kI
∴Q=kP−1I
∴Q=2adj.P
∵q23=−8k
∴2−(3α+4)=−8k⇒k=4
∴∣P∣=2k⇒k=10+6α…(i)
Put value of k in (i).. we get α=−1
⇒α2+k2=17
Let P=[323−10−5−2α0], where α∈R. Suppose Q=[qij] is a matrix satisfying PQ=kI3 for
some non-zero k∈R. If q23=−8k and ∣Q∣=2k2, then α2+k2 is equal to_________.
Held on 24 Feb 2021 · Verified 6 Jul 2026.
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